Difference between revisions of "1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)"
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(Created page with "==Theorem== The following formula holds: $${}_1F_1(a;r;z){}_1F_1(a;r;-z)={}_2F_3\left(a, r-a; r, \dfrac{r}{2}, \dfrac{r}{2}+\dfrac{1}{2}; \dfrac{z^2}{4} \right),$$ where ${}_1...") |
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==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953| | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=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)|next=1F1(a;2a;z)1F1(b;2b;-z)=2F3(a/2+b/2,a/2+b/2+1/2;a+1/2,b+1/2,a+b;z^2/4)}}: $4.2 (5)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 23:25, 3 March 2018
Theorem
The following formula holds: $${}_1F_1(a;r;z){}_1F_1(a;r;-z)={}_2F_3\left(a, r-a; r, \dfrac{r}{2}, \dfrac{r}{2}+\dfrac{1}{2}; \dfrac{z^2}{4} \right),$$ where ${}_1F_1$ denotes hypergeometric 1F1 and ${}_2F_3$ denotes hypergeometric 2F3.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $4.2 (5)$
