Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Some integrals involving associated Legendre functions


Author: S. N. Samaddar
Journal: Math. Comp. 28 (1974), 257-263
MSC: Primary 33A45
MathSciNet review: 0328157
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 33A45

Retrieve articles in all journals with MSC: 33A45


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0328157-4
PII: S 0025-5718(1974)0328157-4
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