On certain slowly convergent series occurring in plate contact problems

Author:
Walter Gautschi

Journal:
Math. Comp. **57** (1991), 325-338

MSC:
Primary 40A05; Secondary 44A10, 73K10, 73T05

MathSciNet review:
1079018

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Abstract | References | Similar Articles | Additional Information

Abstract: A simple computational procedure is developed for accurately summing series of the form , where *z* is complex with and or 3, as well as series of the type

**[1]**Kevin M. Dempsey, Dajin Liu, and John P. Dempsey,*Plana’s summation formula for ∑^{∞}_{𝑚=1,3,\cdots}𝑚⁻²sin(𝑚𝛼),𝑚⁻³cos(𝑚𝛼),𝑚⁻²𝐴^{𝑚},𝑚⁻³𝐴^{𝑚}*, Math. Comp.**55**(1990), no. 192, 693–703. MR**1035929**, 10.1090/S0025-5718-1990-1035929-9**[2]**Walter Gautschi,*On the preceding paper “A Legendre polynomial integral” by James L. Blue*, Math. Comp.**33**(1979), no. 146, 742–743. MR**521288**, 10.1090/S0025-5718-1979-0521288-X**[3]**Walter Gautschi,*Minimal solutions of three-term recurrence relations and orthogonal polynomials*, Math. Comp.**36**(1981), no. 154, 547–554. MR**606512**, 10.1090/S0025-5718-1981-0606512-6**[4]**Walter Gautschi,*On generating orthogonal polynomials*, SIAM J. Sci. Statist. Comput.**3**(1982), no. 3, 289–317. MR**667829**, 10.1137/0903018**[5]**Walter Gautschi,*Questions of numerical condition related to polynomials*, Studies in numerical analysis, MAA Stud. Math., vol. 24, Math. Assoc. America, Washington, DC, 1984, pp. 140–177. MR**925213****[6]**Walter Gautschi,*A class of slowly convergent series and their summation by Gaussian quadrature*, Math. Comp.**57**(1991), no. 195, 309–324. MR**1079017**, 10.1090/S0025-5718-1991-1079017-5**[7]**Walter Gautschi and Gradimir V. Milovanović,*Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series*, Math. Comp.**44**(1985), no. 169, 177–190. MR**771039**, 10.1090/S0025-5718-1985-0771039-1**[8]**E. R. Hansen,*A table of series and products*, Prentice-Hall, Englewood Cliffs, NJ, 1975.**[9]**A. McLellan IV,*Tables of the Riemann zeta function and related functions*, Math. Comp.**22**(1968), Review**69**, 687-688.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1079018-7

Keywords:
Slowly convergent series,
Laplace transformation,
Stieltjes transform,
orthogonal polynomials

Article copyright:
© Copyright 1991
American Mathematical Society