A study of generalized summation theorems for the series 2F1 with an applications to Laplace transforms of convolution type integrals involving Kummer's functions 1F1

Gradimir Milovanovic, Rakesh Parmar, Arjun Rathie
2018 Applicable Analysis and Discrete Mathematics  
Motivated by recent generalizations of classical theorems for the series 2F1 [Integral Transform. Spec. Funct. 229(11), (2011), 823-840] and interesting Laplace transforms of Kummer's confluent hypergeometric functions obtained by Kim et al. [Math. Comput. Modelling 55 (2012), 1068-1071], first we express generalized summations theorems in explicit forms and then by employing these, we derive various new and useful Laplace transforms of convolution type integrals by using product theorem of the
more » ... duct theorem of the Laplace transforms for a pair of Kummer's confluent hypergeometric function.
doi:10.2298/aadm171017002m fatcat:ozvgg444ajgs5exootl3suftui