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Some integrals involving associated Legendre functions

Author: S. N. Samaddar
Journal: Math. Comp. 28 (1974), 257-263
MSC: Primary 33A45
MathSciNet review: 0328157
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Abstract: Calculations of some uncommon integrals involving Legendre functions and their derivatives, which may not be readily evaluated using known results, are presented. Some results show a special type of orthogonality relation in a certain sense. A few of these integrals find their applications in diffraction or scattering problems.

References [Enhancements On Off] (What's this?)

  • [1] S. N. Samaddar, Scattering of Cylindrical Waves by a Spherical Object, Proc. 1971 International Sympos. Antennas and Propagation, Sendai, Japan, Sept. 1-3, 1971, p. 195.
  • [2] P. M. Morse & H. Feshback, Methods of Theoretical Physics. Vol. II, Chap. 11, McGraw-Hill, New York, 1953. MR 15, 583.
  • [3] E. W. Hobson, The Theory of Spherical and Ellipsoidal Harmonies, Chelsea, New York, 1955. MR 16, 356.
  • [4] D. S. Jones, The Theory of Electromagnetism, Internat. Ser. of Monographs on Pure and Appl. Math., vol. 47, Macmillan, New York, 1964. MR 28 #4759. MR 0161555 (28:4759)
  • [5] G. Power, "The associated Legendre polynomial," Math. Gaz., v. 38, 1954, pp. 115-116. MR 15, 701. MR 0060637 (15:701c)

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Keywords: Legendre function, integration by parts, recurrence relations, Rodrigues' formula, Leibnitz theorem for derivatives of products, Kronecker delta, orthogonality
Article copyright: © Copyright 1974 American Mathematical Society

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