pure_python
Pure Python special functions
Bessel–Clifford function.ipynb
| Bessel–Clifford function Cn (argument complex but n restricted to integer instead of complex)
q-analog.ipynb
| q-Pochhammer symbol q_poch
| q-bracket q_bracket
| q-factorial q_factorial
| q-binomial coefficients q_binom
| binomial coefficient binom (using q_binom and without factorial function)
| unilateral basic hypergeometric series q_hyper (accepts all parameters as complex numbers)
| bilateral basic hypergeometric series q_hyper(type=2) (accepts all parameters as complex numbers)
| q-gamma function q_gamma (when q<1, accepts argument as complex number, accepts base q>1)
| first Jackson q-Bessel function q_besselj1 (accepts base q as complex number)
| second Jackson q-Bessel function q_besselj2 (accepts argument and base q as complex numbers)
| third Jackson q-Bessel function q_besselj3 (accepts argument and base q as complex numbers)
| first modified q-Bessel function of the first kind q_besseli1 (accepts argument and base q as complex numbers)
| second modified q-Bessel function of the first kind q_besseli2 (accepts argument and base q as complex numbers)
| third modified q-Bessel function of the first kind q_besseli3 (accepts argument and base q as complex numbers)
| (not implemented) first modified q-Bessel function of the second kind q_besselk1 (not Pure Python, requires sin)
| (not implemented) second modified q-Bessel function of the second kind q_besselk2 (not Pure Python, requires sin)
| Jackson q-difference operator for q-Bessel funtions q_besselj1p q_besselj2p q_besselj3p q_besseli1p q_besseli2p q_besseli3p
| symmetric q-difference operator for q-Bessel funtions q_besselj1p(type=2) q_besselj2p q_besselj3p q_besseli1p q_besseli2p q_besseli3p
| (not implemented) forward difference operator
| (not implemented) backward difference operator
| q-exponential functions e_q and E_q
| q-sine functions q_sin and q_Sin
| q-cosine functions q_cos and q_Cos
subfactorial.ipynb demo only (see treefactorial.py for special functions)
treefactorial.py
| factorial
| binomial coefficient, faster version using treefactorial binom
| subfactorial, fast algorithm subfactorial