Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series

Authors:
Walter Gautschi and Gradimir V. MilovanoviÄ‡

Journal:
Math. Comp. **44** (1985), 177-190, S1

MSC:
Primary 65D32; Secondary 33A65, 65A05, 65B10, 81-08, 82-08

DOI:
https://doi.org/10.1090/S0025-5718-1985-0771039-1

MathSciNet review:
771039

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Abstract: Polynomials , , are constructed which are orthogonal with respect to the weight distributions and , , on . Moment-related methods being inadequate, a discretized Stieltjes procedure is used to generate the coefficients in the recursion formula , , , . The discretization is effected by the Gauss-Laguerre and a composite Fejér quadrature rule, respectively. Numerical values of , as well as associated error constants, are provided for . These allow the construction of Gaussian quadrature formulae, including error terms, with up to 40 points. Examples of *n*-point formulae, , are provided in the supplements section at the end of this issue. Such quadrature formulae may prove useful in solid state physics calculations and can also be applied to sum slowly convergent series.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1985-0771039-1

Article copyright:
© Copyright 1985
American Mathematical Society