Difference between revisions of "Generating relation for Bateman F"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\sum_{k=0}^{\infty} F_n(z)t^n = \dfrac{1}{1-t} {}_2F_1 \left( \dfrac{1}{2}, \dfrac{1+z}{2}; 1; \dfrac{-4t}{(1-t)^2} \ri...") |
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Revision as of 03:03, 22 June 2016
Theorem
The following formula holds: $$\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.
