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 ...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.展开更多
In the theory of Wiman-Valiron on entire function,a theorem on the derivatives of entire functions has important applications to differential equations.We had extended the theorem to the meromorphic functions which ha...In the theory of Wiman-Valiron on entire function,a theorem on the derivatives of entire functions has important applications to differential equations.We had extended the theorem to the meromorphic functions which have finite poles.In this paper we give some applications to linner differential equations and algebraic differential equations.展开更多
文摘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.
文摘In the theory of Wiman-Valiron on entire function,a theorem on the derivatives of entire functions has important applications to differential equations.We had extended the theorem to the meromorphic functions which have finite poles.In this paper we give some applications to linner differential equations and algebraic differential equations.
