Difference between revisions of "Glossary of EM.Cube's Python Functions"

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Line 80: Line 80:
 
| Std. Python function
 
| Std. Python function
 
| Tangent function
 
| Tangent function
−
| -
 
−
|-
 
−
| sec(x)
 
−
| Std. Python function
 
−
| Secant function
 
−
| -
 
−
|-
 
−
| csc(x)
 
−
| Std. Python function
 
−
| Cosecant function
 
−
| -
 
−
|-
 
−
| cot(x)
 
−
| Std. Python function
 
−
| Cotangent function
 
 
| -
 
| -
 
|-
 
|-
Line 115: Line 100:
 
| Std. Python function
 
| Std. Python function
 
| Inverse tangent function
 
| Inverse tangent function
−
| -
 
−
|-
 
−
| asec(x)
 
−
| Std. Python function
 
−
| Inverse secant function
 
−
| -
 
−
|-
 
−
| acsc(x)
 
−
| Std. Python function
 
−
| Inverse cosecant function
 
−
| -
 
−
|-
 
−
| acot(x)
 
−
| Std. Python function
 
−
| Inverse cotangent function
 
 
| -
 
| -
 
|-
 
|-
Line 145: Line 115:
 
| Std. Python function
 
| Std. Python function
 
| Hyperbolic tangent function
 
| Hyperbolic tangent function
−
| -
 
−
|-
 
−
| sech(x)
 
−
| Std. Python function
 
−
| Hyperbolic secant function
 
−
| -
 
−
|-
 
−
| csch(x)
 
−
| Std. Python function
 
−
| Hyperbolic cosecant function
 
−
| -
 
−
|-
 
−
| coth(x)
 
−
| Std. Python function
 
−
| Hyperbolic cotangent function
 
 
| -
 
| -
 
|-
 
|-
Line 177: Line 132:
 
| -
 
| -
 
|-
 
|-
−
| asech(x)
+
| sp.sici(x)
 
| Std. Python function
 
| Std. Python function
−
| Inverse hyperbolic secant function
+
| Sine and cosine integral functions
−
| -
+
−
|-
+
−
| acsch(x)
+
−
| Std. Python function
+
−
| Inverse hyperbolic cosecant function
+
−
| -
+
−
|-
+
−
| acoth(x)
+
−
| Std. Python function
+
−
| Inverse hyperbolic cotangent function
+
−
| -
+
−
|-
+
−
| Ci(x)
+
−
| Std. Python function
+
−
| Cosine integral function
+
 
| See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
 
|-
 
|-
−
| Si(x)
+
| sp.fresnel(x)
−
| Std. Python function
+
−
| Sine integral function
+
−
| See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
+
−
|-
+
−
| C(x)
+
−
| Std. Python function
+
−
| Cosine Fresnel integral function
+
−
| See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
+
−
|-
+
−
| S(x)
+
 
| Std. Python function
 
| Std. Python function
−
| Sine Fresnel integral function
+
| Sine and cosine Fresnel integral functions
 
| See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
 
|-
 
|-
−
| Ellip_E(x)
+
| sp.ellipe(x)
 
| Std. Python function
 
| Std. Python function
 
| Elliptic function of the first kind
 
| Elliptic function of the first kind
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
 
|-
 
|-
−
| Ellip_K(x)
+
| sp.ellipk(x)
 
| Std. Python function
 
| Std. Python function
 
| Elliptic function of the second kind
 
| Elliptic function of the second kind
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
 
|-
 
|-
−
| Ei(x)
+
| sp.expi(x)
 
| Std. Python function
 
| Std. Python function
 
| Exponential integral function
 
| Exponential integral function
 
| See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
 
|-
 
|-
−
| En(n,x)
+
| sp.expn(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Generalized exponential integral function of order n
 
| Generalized exponential integral function of order n
Line 237: Line 167:
 
| -
 
| -
 
|-
 
|-
−
| erf(x)
+
| sp.erf(x)
 
| Std. Python function
 
| Std. Python function
 
| Error function
 
| Error function
 
| See [https://en.wikipedia.org/wiki/Error_function Error Function on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Error_function Error Function on Wikipedia.]
 
|-
 
|-
−
| gamma(x)
+
| sp.erfc(x)
 +
| Std. Python function
 +
| Complementary error function
 +
| See [https://en.wikipedia.org/wiki/Error_function Error Function on Wikipedia.]
 +
|-
 +
| sp.gamma(x)
 
| Std. Python function
 
| Std. Python function
 
| Gamma function
 
| Gamma function
 
| See [https://en.wikipedia.org/wiki/Gamma_function Gamma Function on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Gamma_function Gamma Function on Wikipedia.]
 
|-
 
|-
−
| Airy_A(x)
+
| sp.airy(x)
 
| Std. Python function
 
| Std. Python function
−
| Airy function of the first kind
+
| Airy function of the first (Ai) and second (Bi) kind and their derivatives
 
| See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
 
|-
 
|-
−
| Airy_B(x)
+
| sp.j0(x)
 
| Std. Python function
 
| Std. Python function
−
| Airy function of the second kind
+
| Bessel function of the first kind and order 0
−
| See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
+
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| Jn(n,x)
+
| sp.j1(x)
 +
| Std. Python function
 +
| Bessel function of the first kind and order 1
 +
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 +
|-
 +
| sp.jv(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Bessel function of the first kind and order n
 
| Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| Yn(n,x)
+
| sp.y0(x)
 +
| Std. Python function
 +
| Bessel function of the second kind and order 0
 +
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 +
|-
 +
| sp.y1(x)
 +
| Std. Python function
 +
| Bessel function of the second kind and order 1
 +
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 +
|-
 +
| sp.yv(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Bessel function of the second kind and order n
 
| Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| In(n,x)
+
| sp.i0(x)
 +
| Std. Python function
 +
| Modified Bessel function of the first kind and order 0
 +
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 +
|-
 +
| sp.i1(x)
 +
| Std. Python function
 +
| Modified Bessel function of the first kind and order 1
 +
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 +
|-
 +
| sp.iv(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Modified Bessel function of the first kind and order n
 
| Modified Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| Kn(n,x)
+
| sp.k0(x)
 +
| Std. Python function
 +
| Modified Bessel function of the second kind and order 0
 +
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 +
|-
 +
| sp.k1(x)
 +
| Std. Python function
 +
| Modified Bessel function of the second kind and order 1
 +
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 +
|-
 +
| sp.kv(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Modified Bessel function of the second kind and order n
 
| Modified Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| SB_jn(n,x)
+
| sp.sph_jn(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Spherical Bessel function of the first kind and order n
 
| Spherical Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| SB_yn(n,x)
+
| sp.sph_yn(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Spherical Bessel function of the second kind and order n
 
| Spherical Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| SB_in(n,x)
+
| sp.sph_in(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Modified spherical Bessel function of the first kind and order n
 
| Modified spherical Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| SB_kn(n,x)
+
| sp.sph_kn(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Modified spherical Bessel function of the second kind and order n
 
| Modified spherical Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
−
| Pn(n,x)
+
| sp.lpn(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Legendre function of the first kind and order n
 
| Legendre function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre Polynomials on Wikipedia.]
 
|-
 
|-
−
| Qn(n,x)
+
| sp.lqn(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Legendre function of the second kind and order n
 
| Legendre function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
 
|-
 
|-
−
| Tn(n,x)
+
| sp.lpmn(m,n,x)
 +
| Std. Python function
 +
| Associated Legendre function of the first kind and order n
 +
| See [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre Polynomials on Wikipedia.]
 +
|-
 +
| sp.lqmn(m,n,x)
 +
| Std. Python function
 +
| Associated Legendre function of the second kind and order n
 +
| See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
 +
|-
 +
| sp.eval_chebyt(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Chebyshev polynomial of the first kind and order n
 
| Chebyshev polynomial of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
|-
 
|-
−
| Un(n,x)
+
| sp.eval_chebyu(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Chebyshev polynomial of the second kind and order n
 
| Chebyshev polynomial of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
|-
 
|-
−
| LGn(n,x)
+
| sp.eval_legendre(n,x)
 +
| Std. Python function
 +
| Legendre polynomial of order n
 +
| See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
 +
|-
 +
| sp.eval_laguerre(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Laguerre polynomial of order n
 
| Laguerre polynomial of order n
 
| See [https://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre Polynomials on Wikipedia.]
 
|-
 
|-
−
| Hn(n,x)
+
| sp.eval_hermite(n,x)
 
| Std. Python function
 
| Std. Python function
 
| Hermite polynomial of order n
 
| Hermite polynomial of order n
 
| See [https://en.wikipedia.org/wiki/Hermite_polynomials Hermite Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Hermite_polynomials Hermite Polynomials on Wikipedia.]
−
|-
 
−
| Un(n,x)
 
−
| Std. Python function
 
−
| Hermite-Gauss function of order n
 
−
| -
 
 
|-
 
|-
 
| Math_ce(n,r,x)
 
| Math_ce(n,r,x)
Line 342: Line 322:
 
| See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
 
|-
 
|-
−
| Rect(x)
+
| rect(x)
 
| EMAG Python function
 
| EMAG Python function
 
| Rectangle function
 
| Rectangle function
 
| 1 if |x|≤0.5, 0 elsewhere  
 
| 1 if |x|≤0.5, 0 elsewhere  
 
|-
 
|-
−
| Tri(x)
+
| tri(x)
 
| EMAG Python function
 
| EMAG Python function
 
| Triangle function
 
| Triangle function
 
| 1 if |1-x|≤1, 0 elsewhere  
 
| 1 if |1-x|≤1, 0 elsewhere  
 
|-
 
|-
−
| Spln2(x)
+
| spline2(x)
 
| EMAG Python function
 
| EMAG Python function
 
| Quadratic spline function
 
| Quadratic spline function
 
| -
 
| -
 
|-
 
|-
−
| Spln3(x)
+
| spline3(x)
 
| EMAG Python function
 
| EMAG Python function
 
| Cubic spline function
 
| Cubic spline function
 
| -
 
| -
 
|-
 
|-
−
| Step(x)
+
| step(x)
 
| EMAG Python function
 
| EMAG Python function
 
| Step function
 
| Step function
 
| 1 if x>0, 0 if x<0
 
| 1 if x>0, 0 if x<0
 
|-
 
|-
−
| Haar(x)
+
| ramp(x)
−
| EMAG Python function
+
−
| Haar function
+
−
| sign(x) if |x|<0.5, 0 elsewhere
+
−
|-
+
−
| Ramp(x)
+
 
| EMAG Python function
 
| EMAG Python function
 
| Ramp function
 
| Ramp function
 
| -
 
| -
 
|-
 
|-
−
| Trapz(a,x)
+
| sqr_wave(x)
−
| EMAG Python function
+
−
| Trapezoidal function
+
−
| -
+
−
|-
+
−
| Sqwv(x)
+
 
| EMAG Python function
 
| EMAG Python function
 
| Square wave function
 
| Square wave function
 
| -
 
| -
 
|-
 
|-
−
| Stwv(x)
+
| tri_wave(x)
−
| EMAG Python function
+
−
| Sawtooth wave function
+
−
| -
+
−
|-
+
−
| Trwv(x)
+
 
| EMAG Python function
 
| EMAG Python function
 
| Triangle wave function
 
| Triangle wave function
 
| -
 
| -
 
|-
 
|-
−
| Plstr(d,x)
+
| sawtooth(x)
 
| EMAG Python function
 
| EMAG Python function
−
| Pulse train function with duty cycle d
+
| Sawtooth wave function
 
| -
 
| -
 
|-
 
|-
−
| Sinc(d,x)
+
| sinc(x)
 
| EMAG Python function
 
| EMAG Python function
 
| Sinc function
 
| Sinc function
 
| sin(pi*x)/(pi*x)
 
| sin(pi*x)/(pi*x)
 
|-
 
|-
−
| Fejer(n,x)
+
| rand(x,y)
−
| EMAG Python function
+
−
| Fejer function of order n
+
−
| -
+
−
|-
+
−
| Rand(x)
+
 
| EMAG Python function
 
| EMAG Python function
 
| Random function
 
| Random function

Revision as of 15:05, 29 August 2016

The table below gives a list of all the currently available library functions in EM.Cube:

Syntax Type Description Notes
sign(x) Std. Python function Sign function 1 if x>0, -1 if x<0
fac(x) Std. Python function Factorial For integer values of x: n! = n(n-1)(n-2)...3.2.1
fac2(x) Std. Python function Double factorial For even integer values of x: n!! = n(n-2)(n-4)...4.2, for odd integer values of x: n!! = n(n-2)(n-4)...5.3
ceiling(x) Std. Python function Ceiling function Nearest integer >= x
floor(x) Std. Python function Floor function Nearest integer <= x
power(x,y) Std. Python function Power function x**y
sqrt(x) Std. Python function Square root function x^(1/2)
exp(x) Std. Python function Exponential function e**x
log(x) Std. Python function Natural logarithm function -
log10(x) Std. Python function Base 10 logarithm function ln(x)/ln(10)
log(x,a) Std. Python function Base a logarithm function ln(x)/ln(a)
abs(x) Std. Python function Absolute value function x if x>0, -x if x<0
sin(x) Std. Python function Sine function -
cos(x) Std. Python function Cosine function -
tan(x) Std. Python function Tangent function -
asin(x) Std. Python function Inverse sine function -
acos(x) Std. Python function Inverse cosine function -
atan(x) Std. Python function Inverse tangent function -
atan2(x,y) Std. Python function Inverse tangent function -
sinh(x) Std. Python function Hyperbolic sine function -
cosh(x) Std. Python function Hyperbolic cosine function -
tanh(x) Std. Python function Hyperbolic tangent function -
asinh(x) Std. Python function Inverse hyperbolic sine function -
acosh(x) Std. Python function Inverse hyperbolic cosine function -
atanh(x) Std. Python function Inverse hyperbolic tangent function -
sp.sici(x) Std. Python function Sine and cosine integral functions See Trigonometric Integrals on Wikipedia.
sp.fresnel(x) Std. Python function Sine and cosine Fresnel integral functions See Fresnel Integrals on Wikipedia.
sp.ellipe(x) Std. Python function Elliptic function of the first kind See Elliptic Integrals on Wikipedia.
sp.ellipk(x) Std. Python function Elliptic function of the second kind See Elliptic Integrals on Wikipedia.
sp.expi(x) Std. Python function Exponential integral function See Exponential Integrals on Wikipedia.
sp.expn(n,x) Std. Python function Generalized exponential integral function of order n See Exponential Integrals on Wikipedia.
gauss(x) Std. Python function Gaussian function -
sp.erf(x) Std. Python function Error function See Error Function on Wikipedia.
sp.erfc(x) Std. Python function Complementary error function See Error Function on Wikipedia.
sp.gamma(x) Std. Python function Gamma function See Gamma Function on Wikipedia.
sp.airy(x) Std. Python function Airy function of the first (Ai) and second (Bi) kind and their derivatives See Airy Functions on Wikipedia.
sp.j0(x) Std. Python function Bessel function of the first kind and order 0 See Bessel Functions on Wikipedia.
sp.j1(x) Std. Python function Bessel function of the first kind and order 1 See Bessel Functions on Wikipedia.
sp.jv(n,x) Std. Python function Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
sp.y0(x) Std. Python function Bessel function of the second kind and order 0 See Bessel Functions on Wikipedia.
sp.y1(x) Std. Python function Bessel function of the second kind and order 1 See Bessel Functions on Wikipedia.
sp.yv(n,x) Std. Python function Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
sp.i0(x) Std. Python function Modified Bessel function of the first kind and order 0 See Bessel Functions on Wikipedia.
sp.i1(x) Std. Python function Modified Bessel function of the first kind and order 1 See Bessel Functions on Wikipedia.
sp.iv(n,x) Std. Python function Modified Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
sp.k0(x) Std. Python function Modified Bessel function of the second kind and order 0 See Bessel Functions on Wikipedia.
sp.k1(x) Std. Python function Modified Bessel function of the second kind and order 1 See Bessel Functions on Wikipedia.
sp.kv(n,x) Std. Python function Modified Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
sp.sph_jn(n,x) Std. Python function Spherical Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
sp.sph_yn(n,x) Std. Python function Spherical Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
sp.sph_in(n,x) Std. Python function Modified spherical Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
sp.sph_kn(n,x) Std. Python function Modified spherical Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
sp.lpn(n,x) Std. Python function Legendre function of the first kind and order n See Legendre Polynomials on Wikipedia.
sp.lqn(n,x) Std. Python function Legendre function of the second kind and order n See Legendre Polynomials on Wikipedia.
sp.lpmn(m,n,x) Std. Python function Associated Legendre function of the first kind and order n See Legendre Polynomials on Wikipedia.
sp.lqmn(m,n,x) Std. Python function Associated Legendre function of the second kind and order n See Legendre Polynomials on Wikipedia.
sp.eval_chebyt(n,x) Std. Python function Chebyshev polynomial of the first kind and order n See Chebyshev Polynomials on Wikipedia.
sp.eval_chebyu(n,x) Std. Python function Chebyshev polynomial of the second kind and order n See Chebyshev Polynomials on Wikipedia.
sp.eval_legendre(n,x) Std. Python function Legendre polynomial of order n See Legendre Polynomials on Wikipedia.
sp.eval_laguerre(n,x) Std. Python function Laguerre polynomial of order n See Laguerre Polynomials on Wikipedia.
sp.eval_hermite(n,x) Std. Python function Hermite polynomial of order n See Hermite Polynomials on Wikipedia.
Math_ce(n,r,x) Std. Python function Even periodic (cosine) Mathieu function of order n See Mathieu Functions on Wikipedia.
Math_se(n,r,x) Std. Python function Odd periodic (sine) Mathieu function of order n See Mathieu Functions on Wikipedia.
rect(x) EMAG Python function Rectangle function x|≤0.5, 0 elsewhere
tri(x) EMAG Python function Triangle function 1-x|≤1, 0 elsewhere
spline2(x) EMAG Python function Quadratic spline function -
spline3(x) EMAG Python function Cubic spline function -
step(x) EMAG Python function Step function 1 if x>0, 0 if x<0
ramp(x) EMAG Python function Ramp function -
sqr_wave(x) EMAG Python function Square wave function -
tri_wave(x) EMAG Python function Triangle wave function -
sawtooth(x) EMAG Python function Sawtooth wave function -
sinc(x) EMAG Python function Sinc function sin(pi*x)/(pi*x)
rand(x,y) EMAG Python function Random function -
Z0_MS(e,x) EMAG Python function Characteristic impedance of a microstrip transmission line x: width-to-height ratio, e: substrate permittivity
w_MS(z,e,t) EMAG Python function Width of a microstrip transmission line z: characteristic impedance, e: substrate permittivity, t: substrate thickness
eeff_MS(e,x) EMAG Python function Effective permittivity of a microstrip transmission line x: width-to-height ratio, e: substrate permittivity
woh_MS(e,z) EMAG Python function Width-to-height ratio of a microstrip transmission line z: characteristic impedance z, e: substrate permittivity
Z0_CPW(e,x,y) EMAG Python function Characteristic impedance of a coplanar waveguide transmission line x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
eeff_CPW(e,x,y) EMAG Python function Effective permittivity of a coplanar waveguide transmission line x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
horn_a(d,x,y) EMAG Python function Wavelength-normalized a-dimension of an optimal pyramidal horn antenna d: directivity d, x and y: wavelength-normalized waveguide dimensions
horn_b(d,x,y) EMAG Python function Wavelength-normalized b-dimension of an optimal pyramidal horn antenna d: directivity d, x and y: wavelength-normalized waveguide dimensions
horn_l(d,x,y) EMAG Python function Wavelength-normalized length of an optimal pyramidal horn antenna d: directivity d, x and y: wavelength-normalized waveguide dimensions

 

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