Quick Start

Example 1 — Gamma function:

import numpy as np
from specialfunctions import gamma

print(gamma(5))    # -> 24.0
print(gamma(0.5))  # -> sqrt(π) ≈ 1.7724538509

Example 2 — Bessel functions:

from specialfunctions import bessel_j0, bessel_j1
import numpy as np

x = np.linspace(0, 10, 100)
j0_vals = bessel_j0(x)
j1_vals = bessel_j1(x)
print(f"J0(0) = {bessel_j0(0.0)}")  # -> 1.0
print(f"J1(0) = {bessel_j1(0.0)}")  # -> 0.0

Example 3 — Error functions:

from specialfunctions import erf, erfc, erfinv
import numpy as np

print(erf(1.0))      # -> 0.8427007929
print(erfc(1.0))     # -> 0.1572992071
print(erfinv(0.5))   # -> 0.4769362762

Example 4 — Orthogonal polynomials:

from specialfunctions import legendre_poly, chebyshev_t
import numpy as np

x = np.linspace(-1, 1, 50)
p3 = legendre_poly(3, x)      # Legendre P_3(x)
t4 = chebyshev_t(4, x)        # Chebyshev T_4(x)