Difference between revisions of "Hypergeometric 1F1"

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=Properties=
 
=Properties=
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[[1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)]]<br />
  
 
=References=
 
=References=

Revision as of 20:30, 17 June 2017

The hypergeometric function ${}_1F_1$ (sometimes denoted by $M$, sometimes called the confluent hypergeometric function of the first kind) is defined by the series $${}_1F_1(a;b;z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(a)_k z^k}{(b)_k k!},$$ where $(a)_k$ denotes the Pochhammer symbol and $k!$ denotes the factorial.

Properties

1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)

References

Hypergeometric functions