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 …

In the present review, we deal with the recently introduced method of spectral parameter
power series (SPPS) and show how its application leads to an explicit form of the …

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 …

Consider the Sturm–Liouville equation− y′′+ q (x) y= ρ 2 yy & amp;# x0005E; ′ ′
& amp;# x0002B; q (x) y& amp;# x0003D; ρ & amp;# x0005E; 2y with a real …

An L-basis associated to a linear second-order ordinary differential operator L is an infinite
sequence of functions [Formula: see text] such that Lφk= 0 for k= 0, 1, Lφk= k (k− 1) φk− 2 …

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 …