๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A generalized formula for the integral of three associated Legendre polynomials

โœ Scribed by H.A. Mavromatis; R.S. Alassar

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
253 KB
Volume
12
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this paper, a generalized formula for the definite integral of three associated Legendre polynomials of the first kind that arises in various physical applications is given in terms of the 3F2 hypergeometric function and the 3 -j symbols. The special case, when the integral reduces to a particularly simple familiar expression, is also mentioned. (~

๐Ÿ“œ SIMILAR VOLUMES

The overlap integral of three associated
The overlap integral of three associated Legendre polynomials
โœ Shi-hai Dong; R. Lemus ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 327 KB

A closed formula with a double sum is obtained for the overlap integral of three associated Legendre polynomials (ALPS). The result is applicable to integral involving the ALP with arbitrary degree 1 and order m. Special overlap integrals, including the cases mg = ml + rn2 or Irnl -rnzl, are present

A Combinatorial Formula for the Associat
A Combinatorial Formula for the Associated Legendre Functions of Integer Degree
โœ J.F. van Diejen; A.N. Kirillov ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 552 KB

dedicated to professor richard a. askey on the occasion of his 65th birthday We apply inverse scattering theory to a Schro dinger operator with a regular reflectionless Po schl Teller potential on the line, to arrive at a combinatorial formula for the associated Legendre functions of integer degree

A general formula for three-point bend s
A general formula for three-point bend specimen J-integral calculation
โœ D.Z Zhang; J Lin ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 286 KB

## This article gives a general formula for three-point bend specimen J-integral calculation. This formula can be used when q,/W 2 0.5, as the well known formula J = A/Eb .&,/IV) given in standard ASTM E8 13-8 1, and can also be used when q,/ W < 0.5. Therefore it is very useful for practical use.

A Combinatorial Formula for the Lineariz
A Combinatorial Formula for the Linearization Coefficients of General Sheffer Polynomials
โœ Dongsu Kim; Jiang Zeng ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 341 KB

We prove a formula for the linearization coefficients of the general Sheffer polynomials, which unifies all the special known results for Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. Furthermore, we give a new and explicit real version of the corresponding formula for Meix