SciPy — Special Functions

Bessel functions

from scipy.special import jv, yv, kn
import numpy as np

x = np.linspace(0, 10, 100)

# Bessel functions of first kind
j0 = jv(0, x)
j1 = jv(1, x)

# Bessel functions of second kind
y0 = yv(0, x)

Gamma function

from scipy.special import gamma, gammaln

print(f"Gamma(5) = {gamma(5):.4f}")  # 4! = 24
print(f"ln(Gamma(5)) = {gammaln(5):.4f}")

Beta function

from scipy.special import beta

print(f"Beta(2, 3) = {beta(2, 3):.4f}")

Error function

from scipy.special import erf, erfc

print(f"erf(0) = {erf(0):.4f}")
print(f"erf(1) = {erf(1):.4f}")
print(f"erfc(1) = {erfc(1):.4f}")

Exponential integrals

from scipy.special import expi, exp1

print(f"Ei(1) = {expi(1):.4f}")
print(f"E1(1) = {exp1(1):.4f}")

Zeta function

from scipy.special import zeta

print(f"Zeta(2) = {zeta(2):.4f}")  # π²/6

Elliptic functions

from scipy.special import ellipk, ellipe

m = 0.5
print(f"K(m) = {ellipk(m):.4f}")
print(f"E(m) = {ellipe(m):.4f}")

Mini Practice

1. Compute Bessel functions
2. Evaluate gamma function
3. Calculate error function
4. Explore zeta function

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