On a finite sum involving inverse powers of cosines

DOI10.1007/s10440-011-9612-zzbMath1230.11031OpenAlexW1991269238MaRDI QIDQ634689

Victor Kowalenko

Publication date: 16 August 2011

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-011-9612-z

zbMATH Keywords

Riemann zeta functionasymptoticsapproximationdivergent seriesBernoulli numbersdigamma functioncosecant numbersinverse powers of cosinespartition method for a power series expansion

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Power series (including lacunary series) in one complex variable (30B10) Approximation in the complex plane (30E10) Approximate quadratures (41A55) Special sequences and polynomials (11B83) Numerical summation of series (65B10) Analytic theory of partitions (11P82) Discrete mathematics in relation to computer science (68R99)

Related Items (6)

Further developments of basic trigonometric power sums ⋮ Trigonometric sums and Riemann zeta function ⋮ Generalized cosecant numbers and trigonometric inverse power sums ⋮ Basic trigonometric power sums with applications ⋮ Explicit expressions for finite trigonometric sums ⋮ Trigonometric sums by Hermite interpolations

Uses Software

• Mathematica

Cites Work

• Properties and applications of the reciprocal logarithm numbers
• Generalizing the reciprocal logarithm numbers by adapting the partition method for a power series expansion
• Exactification of the asymptotics for Bessel and Hankel functions.
• Applications of the cosecant and related numbers
• The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation
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