| style="width:150px;" | Std. Python function
| style="width:270px;" | Sine and cosine integral functions
| style="width:270px;" | See see [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
|-
| sp.fresnel(x)
| Std. Python function
| Sine and cosine Fresnel integral functions
| See see [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
|-
| sp.ellipe(x)
| Std. Python function
| Elliptic function of the first kind
| See see [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
|-
| sp.ellipk(x)
| Std. Python function
| Elliptic function of the second kind
| See see [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
|-
| sp.expi(x)
| Std. Python function
| Exponential integral function
| See see [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
|-
| sp.expn(n,x)
| Std. Python function
| Generalized exponential integral function of order n
| See see [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
|-
| sp.erf(x)
| Std. Python function
| Error function
| See see [https://en.wikipedia.org/wiki/Error_function Error Function on Wikipedia.]
|-
| sp.erfc(x)
| Std. Python function
| Complementary error function
| See see [https://en.wikipedia.org/wiki/Error_function Error Function on Wikipedia.]
|-
| sp.gamma(x)
| Std. Python function
| Gamma function
| See see [https://en.wikipedia.org/wiki/Gamma_function Gamma Function on Wikipedia.]
|-
| sp.airy(x)
| Std. Python function
| Airy function of the first (Ai) and second (Bi) kind and their derivatives
| See see [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
|-
| sp.j0(x)
| Std. Python function
| Bessel function of the first kind and order 0
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.j1(x)
| Std. Python function
| Bessel function of the first kind and order 1
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.jv(n,x)
| Std. Python function
| Bessel function of the first kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.y0(x)
| Std. Python function
| Bessel function of the second kind and order 0
| See 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 see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.yv(n,x)
| Std. Python function
| Bessel function of the second kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.i0(x)
| Std. Python function
| Modified Bessel function of the first kind and order 0
| See 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 see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.iv(n,x)
| Std. Python function
| Modified Bessel function of the first kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.k0(x)
| Std. Python function
| Modified Bessel function of the second kind and order 0
| See 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 see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.kv(n,x)
| Std. Python function
| Modified Bessel function of the second kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.sph_jn(n,x)
| Std. Python function
| Spherical Bessel function of the first kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.sph_yn(n,x)
| Std. Python function
| Spherical Bessel function of the second kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.sph_in(n,x)
| Std. Python function
| Modified spherical Bessel function of the first kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.sph_kn(n,x)
| Std. Python function
| Modified spherical Bessel function of the second kind and order n
| See see [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
|-
| sp.lpn(n,x)
| Std. Python function
| Legendre function of the first kind and order n
| See see [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre Polynomials on Wikipedia.]
|-
| sp.lqn(n,x)
| Std. Python function
| Legendre function of the second kind and order n
| See see [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
|-
| sp.lpmn(m,n,x)
| Std. Python function
| Associated Legendre function of the first kind and order n
| See 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 see [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
|-
| sp.eval_chebyt(n,x)
| Std. Python function
| Chebyshev polynomial of the first kind and order n
| See see [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
|-
| sp.eval_chebyu(n,x)
| Std. Python function
| Chebyshev polynomial of the second kind and order n
| See see [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
|-
| sp.eval_legendre(n,x)
| Std. Python function
| Legendre polynomial of order n
| See see [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
|-
| sp.eval_laguerre(n,x)
| Std. Python function
| Laguerre polynomial of order n
| See see [https://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre Polynomials on Wikipedia.]
|-
| sp.eval_hermite(n,x)
| Std. Python function
| Hermite polynomial of order n
| See see [https://en.wikipedia.org/wiki/Hermite_polynomials Hermite Polynomials on Wikipedia.]
|-
| Math_ce(n,r,x)
| Std. Python function
| Even periodic (cosine) Mathieu function of order n
| See see [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
|-
| Math_se(n,r,x)
| Std. Python function
| Odd periodic (sine) Mathieu function of order n
| See see [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
|}