A Legendre polynomial integral

Author:
James L. Blue

Journal:
Math. Comp. **33** (1979), 739-741

MSC:
Primary 65D30; Secondary 33A45

MathSciNet review:
521287

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Abstract: Let be the usual Legendre polynomials. The following integral is apparently new.

**[1]**Philip J. Davis and Philip Rabinowitz,*Numerical integration*, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR**0211604****[2]**Gene H. Golub and John H. Welsch,*Calculation of Gauss quadrature rules*, Math. Comp. 23 (1969), 221-230; addendum, ibid.**23**(1969), no. 106, loose microfiche suppl, A1–A10. MR**0245201**, 10.1090/S0025-5718-69-99647-1**[3]**Walter Gautschi,*On the construction of Gaussian quadrature rules from modified moments.*, Math. Comp.**24**(1970), 245–260. MR**0285117**, 10.1090/S0025-5718-1970-0285117-6**[4]**R. A. Sack and A. F. Donovan,*An algorithm for Gaussian quadrature given modified moments*, Numer. Math.**18**(1971/72), 465–478. MR**0303693****[5]**U. HOCHSTRASSER, "Orthogonal polynomials," in M. Abramowitz and I. A. Stegun (eds.),*Handbook of Mathematical Functions*, Dover, New York, 1965.**[6]**W. S. BROWN,*Altran User's Manual*, 4th ed., Bell Laboratories, Murray Hill, N. J., 1977.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0521287-8

Article copyright:
© Copyright 1979
American Mathematical Society