Difference between revisions of "Hypergeometric 3F2"
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(Created page with "The hypergeometric function ${}_3F_2$ is defined by $${}_3F_2(a_1,a_2,a_3; b_1,b_2; z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k(a_3)_k}{(b_1)_k(b_2)_k(b_3)_k}...") |
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=Properties= | =Properties= | ||
| − | [[2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2, | + | [[2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)]] <br /> |
=References= | =References= | ||
Latest revision as of 20:21, 17 June 2017
The hypergeometric function ${}_3F_2$ is defined by $${}_3F_2(a_1,a_2,a_3; b_1,b_2; z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1)_k(a_2)_k(a_3)_k}{(b_1)_k(b_2)_k(b_3)_k} \dfrac{z^k}{k!},$$ where $(a)_k$ denotes the Pochhammer symbol.
Properties
2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
