Difference between revisions of "Hypergeometric 4F1"
From specialfunctionswiki
(Created page with "The hypergeometric ${}_4F_1$ function is defined by the series $${}_4F_1(a_1,a_2,a_3,a_4;b_1;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k(a_3)_k(a_4)_k}{(b_1)_k}...") |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 4: | Line 4: | ||
=Properties= | =Properties= | ||
| + | [[2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2)]]<br /> | ||
=References= | =References= | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
| + | |||
| + | {{:Hypergeometric functions footer}} | ||
Latest revision as of 20:27, 17 June 2017
The hypergeometric ${}_4F_1$ function is defined by the series $${}_4F_1(a_1,a_2,a_3,a_4;b_1;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k(a_3)_k(a_4)_k}{(b_1)_k} \dfrac{z^k}{k!},$$ where $(a_1)_k$ denotes the Pochhammer symbol.
Properties
2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2)
