The summation of series of special functions (or, accepting Turán's intervention,“useful
functions”) is a subdiscipline of Classical Analysis. Functional series built from members of …

Bearing in mind an increasing popularity of the fractional calculus the main aim of this paper
is to derive several new representation formulae for the cumulative distribution function (cdf) …

It is known that the Struve function H ν and the modified Struve function L ν are closely
connected to the Bessel function of the first kind J ν and to the modified Bessel function of …

The principal aim of this paper is to introduce the extended Voigt-type function V μ, ν (x, y)
and its counterpart extension W μ, ν (x, y), involving the Neumann function Y ν in the kernel …

The main objective of this paper is to present a new extension of the familiar Mathieu series
and the alternating Mathieu series S (r) and S~(r) which are denoted by S μ, ν (r) and S~ μ, ν …

Full article: Neumann series and Lommel functions of two variables Skip to Main Content
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Discrete Chebyshev-type inequalities are established for sequences of modified Bessel
functions of the first and second kind, recognizing that the sums involved are actually …

The main aim of this article is to derive three new formulas for the cumulative distribution
function of the noncentral chi-square distribution. The main advantage of such formulas is …

In the 18th century, it became clear that the existing elementary functions are not sufficient to
describe a number of unsolved problems in various branches of mathematics and physics …

The main aim of this article is to establish a closed-form expression for the Neumann series
built with Macdonald functions in which order contains the summation index and the …