Integration formulae involving derivatives

Author:
T. N. L. Patterson

Journal:
Math. Comp. **23** (1969), 411-412

MSC:
Primary 65.55

DOI:
https://doi.org/10.1090/S0025-5718-1969-0242371-6

Corrigendum:
Math. Comp. **24** (1970), 243.

MathSciNet review:
0242371

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Abstract: A method, developed by Hammer and Wicke, for deriving high precision integration formulae involving derivatives is modified. It is shown how such formulae may be simply derived in terms of well-known polynomials.

**[1]**A. H. Stroud & D. D. Stancu, ``Quadrature formulas with multiple Gaussian modes,''*J. Soc. Indust. Appl. Math., Ser. B, Numer. Anal.*, v. 2, 1965, pp. 129-143. MR**31**#4177. MR**0179940 (31:4177)****[2]**P. C. Hammer & H. H. Wicke, ``Quadrature formulas involving derivatives of the integrand,''*Math. Comp.*, v. 14, 1960, pp. 3-7. MR**22**#1073. MR**0110191 (22:1073)****[3]**G. W. Struble, ``Tables for use in quadrature formulas involving derivatives of the integrand,''*Math. Comp.*, v. 14, 1960, pp. 8-12. MR**22**#1074. MR**0110192 (22:1074)****[4]**V. I. Krylov,*Approximate Calculation of Integrals, Fizmatgiz*, Moscow, 1959; English transl., Macmillan, New York, 1962. MR**22**#2002; MR**26**#2008. MR**0144464 (26:2008)****[5]**A. H. Stroud & D. Secrest,*Gaussian Quadrature Formulas*, Prentice-Hall, Englewood Cliffs, N. J., 1966, 374 pp. MR**34**#2185. MR**0202312 (34:2185)**

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0242371-6

Article copyright:
© Copyright 1969
American Mathematical Society