scholarly journals Expansion of a class of functions into an integral involving associated Legendre functions

1994 ◽  
Vol 17 (2) ◽  
pp. 293-300
Author(s):  
Nanigopal Mandal ◽  
B. N. Mandal
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Mathematical Physics ◽  
Legendre Functions ◽  
Expansion Formula ◽  
Associated Legendre Functions ◽  
General Integral ◽  
Class Of Functions

A theorem for expansion of a class of functions into an integral involving associated Legendre functions is obtained in this paper. This is a somewhat general integral expansion formula for a functionf(x)defined in(x1,x2)where-1<x1<x2<1, which is perhaps useful in solving certain boundary value problems of mathematical physics and of elasticity involving conical boundaries.

scholarly journals Spatially Restricted Integrals in Gradiometric Boundary Value Problems

2009 ◽  
Vol 44 (4) ◽  
pp. 131-148 ◽  
Author(s):  
M. Eshagh
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Legendre Functions ◽  
Gravity Gradiometry ◽  
Satellite Gravity Gradiometry ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Associated Legendre Functions ◽  
Tensor Spherical Harmonics ◽  
Slepian Functions

Spatially Restricted Integrals in Gradiometric Boundary Value ProblemsThe spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve spatially restricted integral products of scalar, vector and tensor spherical harmonics. This paper formulates these integrals in terms of combinations of the Gaunt coefficients and integrals of associated Legendre functions. The presented formulas for these integrals are useful in recovering the Earth's gravity field locally from the satellite gravity gradiometry data.

Boundary Value Problems of Mathematical Physics, Vol. I

1968 ◽  
Vol 22 (101) ◽  
pp. 223
Author(s):  
Hans F. Weinberger ◽  
Ivar Stakgold
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Mathematical Physics

scholarly journals Legendre functions of fractional degree: transformations and evaluations

2016 ◽  
Vol 472 (2188) ◽  
pp. 20160097 ◽  
Author(s):  
Robert S. Maier
Keyword(s):  
Boundary Value Problems ◽  
Algebraic Curves ◽  
Applied Mathematics ◽  
Classical Case ◽  
Elliptic Integrals ◽  
Legendre Functions ◽  
Coordinate Transformations ◽  
Symbolic Manipulation ◽  
Associated Legendre Functions ◽  
Complete Elliptic Integrals

Associated Legendre functions of fractional degree appear in the solution of boundary value problems on wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer, they can be expressed using complete elliptic integrals. In this study, many transformations are derived, which reduce the case when the degree differs from an integer by one-third, one-fourth or one-sixth to the classical case. These transformations or identities facilitate the symbolic manipulation and evaluation of Legendre and Ferrers functions. They generalize both Ramanujan's transformations of elliptic integrals and Whipple's formula, which relates Legendre functions of the first and second kinds. The proofs employ algebraic coordinate transformations, specified by algebraic curves.

Boundary Value Problems of Mathematical Physics, Vol. 1

Physics Today ◽  
1967 ◽  
Vol 20 (12) ◽  
pp. 89-91 ◽  
Author(s):  
Ivan Stakgold ◽  
George H. Weiss
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Mathematical Physics
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