Some Unified and Generalized Kummer's Second Summation Theorems with Applications in Laplace Transform Technique
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Keywords:
Gauss and Kummer hypergeometric functions, Legendre duplication formula, Pfaff-Kummer's linear hypergeometric transformation, Principle of analytic continuation, Laplace transformsAbstract
Some significant hypergeometric summation theorems with suitable convergence conditions, are obtained in the present study; analogous to summation theorems for Gauss function ${_2F_1(\frac{1}{2})}$ presented by Brychkov, Prudnikov et~al. and derived by Fox, Rakha-Rathie. By means of these summation theorems we also find the Laplace transforms of Kummer's confluent hypergeometric function $_1F_1$ in closed form.
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