Results 41 to 50 of about 8,602 (292)
On Legendre functions of imaginary degree and associated integral transforms [PDF]
, 2003 New integral representations, asymptotic formulas, and series expansions in powers of tanh(t/2) are obtained for the imaginary and real parts of the Legendre function Piξ(cosht).
Malits, P.
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AdS7 black-hole entropy and 5D N $$ \mathcal{N} $$ = 2 Yang-Mills
Journal of High Energy Physics, 2020 We generalise the work of 1810.11442 for the case of AdS7/CFT5. Starting from the 2-equivalent charge, 3-equivalent rotation non-extremal black-hole solution in 7D gauged supergravity, we consider the supersymmetric and then the extremal limit and ...
G. Kántor +2 more
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ISSM-SESAW v1.0: mesh-based computation of gravitationally consistent sea-level and geodetic signatures caused by cryosphere and climate driven mass change [PDF]
Geoscientific Model Development, 2016 A classical Green's function approach for computing gravitationally consistent sea-level variations associated with mass redistribution on the earth's surface employed in contemporary sea-level models naturally suits the spectral methods for numerical ...
S. Adhikari, E. R. Ivins, E. Larour
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A simple construction of a fundamental solution for the extended Weinstein equation
CuboIn this article, we study the extended Weinstein equation \[ Lu=\Delta u+\frac{k}{x_n}\frac{\partial u}{\partial x_n}+\frac{\ell}{x_n^2}u, \] where \(u\) is a sufficiently smooth function defined in \(\mathbb{R}^n\) with \(x_n>0\) and \(n\ge 3\).
Sirkka-Liisa Eriksson, Heikki Orelma
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On Legendre numbers of the second kind
International Journal of Mathematics and Mathematical Sciences, 1988 The Legendre numbers of the second kind, an infinite set of rational numbers, are defined from the associated Legendre functions. An explicit formula and a partial table for these numbers are given and many elementary properties are presented.
Paul W. Haggard
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Inequalities for the Associated Legendre Functions
Journal of Approximation Theory, 1998 The main results are about the bound for the associated Legendre functions of the first kind \(P_n^m(x)\) with fixed \(x\in [-1,1]\) and integer \(m,n,1\leq | m| \leq n.\) First of all, the author proves a result about transferring upper bounds of the Legendre polynomials \(P_n(x)\) to the functions \(P_n^m(x).\) That result allows to obtain bounds of ...
openaire +2 more sources
On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
International Journal of Mathematics and Mathematical Sciences, 2007 We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer.
Stamatis Koumandos
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Entropy, 2020 In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
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Advanced Engineering Materials, EarlyView.Grain boundary triple junctions are an essential ingredient of the microstructure of polycrystalline materials. In this study, a triple junction is observed using atomic‐resolution scanning transmission electron microscopy and characterized. Computer simulations reveal that the junction has a dislocation character that is determined by the joining ...
Tobias Brink +4 more
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A generalized formula for the integral of three associated Legendre polynomials [PDF]
, 1999 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
Alassar, R.S., Mavromatis, H.A.
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