Difference between revisions of "Hypergeometric 4F1"

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(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}...")
 
 
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=Properties=
 
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[[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]]
 
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{{: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)

References

Hypergeometric functions