Difference between revisions of "Generating relation for Bateman F"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\sum_{k=0}^{\infty} F_n(z)t^n = \dfrac{1}{1-t} {}_2F_1 \left( \dfrac{1}{2}, \dfrac{1+z}{2}; 1; \dfrac{-4t}{(1-t)^2} \ri...") |
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==References== | ==References== | ||
| + | * {{BookReference|Special Functions|1960|Earl David Rainville|prev=Bateman F|next=Three-term recurrence for Bateman F}}: $148. (2)$ | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 03:05, 22 June 2016
Theorem
The following formula holds: $$\displaystyle\sum_{k=0}^{\infty} F_n(z)t^n = \dfrac{1}{1-t} {}_2F_1 \left( \dfrac{1}{2}, \dfrac{1+z}{2}; 1; \dfrac{-4t}{(1-t)^2} \right),$$ where $F_n$ denotes the Bateman F and ${}_2F_1$ denotes the hypergeometric pFq.
Proof
References
- 1960: Earl David Rainville: Special Functions ... (previous) ... (next): $148. (2)$
