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!



Laplace transform of : $t^{\gamma-1} F(\alpha,\beta,\delta,t)$, where $F$ is the Gauss' hypergeometric function
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. 


