Difference between revisions of "Hypergeometric 1F1"
From specialfunctionswiki
| Line 4: | Line 4: | ||
=Properties= | =Properties= | ||
| + | [[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)
