Dirichlet series
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11—14 of 14 matching pages
11: 25.11 Hurwitz Zeta Function
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►The function was introduced in Hurwitz (1882) and defined by the series expansion
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§25.11(iv) Series Representations
… ►For other series expansions similar to (25.11.10) see Coffey (2008). … ►§25.11(x) Further Series Representations
… ► …12: Errata
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Section 27.11
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Equation (25.15.10)
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Equations (14.13.1), (14.13.2)
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Subsection 25.2(ii) Other Infinite Series
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Equation (25.11.36)
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25.15.10
The upper-index of the finite sum which originally was , was replaced with since .
Reported by Gergő Nemes on 2021-08-23
Originally it was stated that these Fourier series converge “…conditionally when is real and .” It has been corrected to read “If then they converge, but, if , they do not converge absolutely.”
Reported by Hans Volkmer on 2021-06-04
13: Bibliography G
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Contiguous relations and summation and transformation formulae for basic hypergeometric series.
J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
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Basic Hypergeometric Series.
Encyclopedia of Mathematics and its Applications, Vol. 35, Cambridge University Press, Cambridge.
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Formulas of the Dirichlet-Mehler Type.
In Fractional Calculus and its Applications, B. Ross (Ed.),
Lecture Notes in Math., Vol. 457, pp. 207–215.
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Dirichlet convolution of cotangent numbers and relative class number formulas.
Monatsh. Math. 110 (3-4), pp. 231–256.
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Multilateral summation theorems for ordinary and basic hypergeometric series in
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SIAM J. Math. Anal. 18 (6), pp. 1576–1596.
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14: Bibliography J
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Bounds on Dawson’s integral occurring in the analysis of a line distribution network for electric vehicles.
Eurandom Preprint Series
Technical Report 14, Eurandom, Eindhoven, The Netherlands.
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Differential equations and mathematical biology.
Chapman & Hall/CRC Mathematical and Computational Biology
Series, CRC Press, Boca Raton, FL.
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Differential equations and mathematical biology.
Chapman & Hall/CRC Mathematical Biology and Medicine Series, Chapman & Hall/CRC, Boca Raton, FL.
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The Theory of Electromagnetism.
International Series of Monographs on Pure and Applied
Mathematics, Vol. 47. A Pergamon Press Book, The Macmillan Co., New York.
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The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis.
J. Reine Angew. Math. 583, pp. 29–86.
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