In the present work, a unification of certain functions of mathematical physics is proposed and its properties are studied. The proposed function unifies Lommel function, Struve function, the Bessel-Maitland function and its generalization, Dotsenko function, generalized Mittag-Leffler function etc. The properties include absolute and uniform convergence, differential recurrence relation, integral representations in the form of Euler-Beta transform, Mellin-Barnes transform, Laplace transform and Whittaker transform. The special cases namely the generalized hypergeometric function, generalized Laguerre polynomial, Fox H-function etc. are also obtained.
A. K. Shukla and J. C. Prajapti, “On a Generlization of Mittag-Leffler Functions and Its Properties,” Journal of Mathematical Analysis and Applications, Vol. 336, No. 2, 2007, pp. 797-811. doi:10.1016/j.jmaa.2007.03.018
R. Gorenflo, A. A. Kilbas and S. V. Rogosin, “On the Generalized Mittag-Leffler Type Function,” Integral Transforms and Special Functions, Vol. 7, No. 3-4, 1998, pp. 215-224. doi:10.1080/10652469808819200