Difference between revisions of "(c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0"
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(Created page with "==Theorem== The following formula holds: $$(c-a-b){}_2F_1(a,b;c;z)-(c-a){}_2F_1(a-1,b;c;z)+b(1-z){}_2F_1(a,b+1;c;z)=0,$$ where ${}_2F_1$ denotes hypergeometric 2F1. ==Pro...") |
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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=(c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0|next=}}: $\S 2.8 (36)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 23:24, 3 March 2018
Theorem
The following formula holds: $$(c-a-b){}_2F_1(a,b;c;z)-(c-a){}_2F_1(a-1,b;c;z)+b(1-z){}_2F_1(a,b+1;c;z)=0,$$ where ${}_2F_1$ denotes hypergeometric 2F1.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous): $\S 2.8 (36)$
