What is the Laplace transform of : $t^{\gamma-1} F(\alpha,\beta,\delta,t)$, where $\gamma >0 $ and $F$ is the Gauss' hypergeometric function.
Thanks!
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Sign up to join this communityWhat is the Laplace transform of : $t^{\gamma-1} F(\alpha,\beta,\delta,t)$, where $\gamma >0 $ and $F$ is the Gauss' hypergeometric function.
Thanks!
There is an explicit formula in the book: A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev. INTEGRALS AND SERIES, Volume 4. Direct Laplace Transforms. GORDON AND BREACH, 1992.
It is on the page 533 and is in terms of $_{2}F_{2}$ hypergeometric function. For special values of parameters for sure it can be simplified using the same book volume 3.