Ordinary differential operators and the integral representation of sums of certain power series

DOI10.1090/mosc/294zbMath1443.33034OpenAlexW3014796325MaRDI QIDQ4960300

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Publication date: 14 April 2020

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mosc/294

zbMATH Keywords

Green's functionRiemann \(\zeta\)-functionEuler digamma functionintegral representation of power seriespolylogarithms and associated functions

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Power series (including lacunary series) in one complex variable (30B10) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Green's functions for ordinary differential equations (34B27) Other functions defined by series and integrals (33E20)

Related Items (4)

Polynomials in the differentiation operator and formulas for the sums of certain convergent series ⋮ Values of the Riemann zeta function and the Dirichlet beta function at positive integer points and multiple numerical series ⋮ Lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials ⋮ Integral representation of sums of series associated with special functions

Cites Work

• Integral representations of the Riemann zeta function for odd-integer arguments
• Green's function of ordinary differential operators and an integral representation of sums of certain power series
• On integral representation of sums of some power series
• New integral representations of the polylogarithm function
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