Transmutations, Singular and Fractional Differential Equations with Applications to
Mathematical Physics connects difficult problems with similar more simple ones. The book's …

This book provides an introduction to the most recent developments in the theory and
practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A …

A new representation of solutions to the equation− y′′+ q (x) y= ω 2 y is obtained. For
every x the solution is represented as a Neumann series of Bessel functions depending on …

This textbook provides a thorough overview of mathematical physics, highlighting classical
topics as well as recent developments. Readers will be introduced to a variety of methods …

A new representation for a regular solution of the perturbed Bessel equation of the form is
obtained. The solution is represented as a Neumann series of Bessel functions uniformly …

A spectral parameter power series (SPPS) representation for regular solutions of singular
Bessel type Sturm–Liouville equations with complex coefficients is obtained as well as an …

A method for approximate solution of spectral problems for Sturm–Liouville equations based
on the construction of the Delsarte transmutation operators is presented. In fact the problem …

A Neumann series of Bessel functions (NSBF) representation for solutions of Sturm–
Liouville equations and for their derivatives is obtained. The representation possesses an …

A representation for integral kernels of Delsarte transmutation operators is obtained in the
form of a functional series with exact formulae for the terms of the series. It is based on the …

This is a brief overview of some recent developments in the transmutation operator
approach to practical solution of mathematical physics problems. It introduces basic notions …