Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell2010 |
See Shaw, Ewart "Hypergeometric Functions and CDFs in J".
Documentation
:: (Ord a, Fractional a) | |
=> [a] | \( a_1,\ldots,a_p \) |
-> [a] | \( b_1,\ldots,b_q \) |
-> a | \( z \) |
-> a |
\( _pF_q(a_1,\ldots,a_p;b_1,\ldots,b_q;z) = \displaystyle\sum_{n=0}^\infty\frac{(a_1)_n\cdots(a_p)_n}{(b_1)_b\cdots(b_q)_n}\frac{z^n}{n!} \)
The radius of convergence is
\( \rho = \begin{cases} \infty & \text{if} & p<q+1 \\ 1 & \text{if} & p=q+1 \\ 0 & \text{if} & p>q+1 \\ \end{cases} \)
This iterates until the result stabilizes.
Euler's transform:
\( \displaystyle _2F_1(a,b;c;z) = (1-z)^{-a} {}_2F_1\left(a,c-b;c;\frac{z}{z-1}\right) \)
Koekoek, Roelef and Swarttouw, René F. The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue.
Since: 0.1.5.0