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Multi-Integral Representations for Associated Legendre and Ferrers Functions [PDF]
Symmetry, 2020 For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result of the determination of these formulae, we compute some
Howard Cohl +2 more
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Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials [PDF]
Mathematics, 2021 In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are ...
Abdel Moneim Y. Lashin +2 more
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Inequalities for the Associated Legendre Functions [PDF]
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 ...
Lohöfer, G.
openaire +3 more sources
The Study of Triple Integral Equations with Generalized Legendre Functions [PDF]
Abstract and Applied Analysis, 2008 A method is developed for solutions of two sets of triple integral equations involving associated Legendre functions of imaginary arguments. The solution of each set of triple integral equations involving associated Legendre functions is reduced to a ...
B. M. Singh, J. Rokne, R. S. Dhaliwal
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Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations [PDF]
Communications, 2010 In applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre
Vladimir Guldan, Mariana Marcokova
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On Parameter Differentiation for Integral Representations of Associated Legendre Functions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters.
Howard S. Cohl
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Expansion of a class of functions into an integral involving associated Legendre functions [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 A theorem for expansion of a class of functions into an integral involving associated Legendre functions is obtained in this paper.
Nanigopal Mandal, B. N. Mandal
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Some applications of Legendre numbers [PDF]
International Journal of Mathematics and Mathematical Sciences, 1988 The associated Legendre functions are defined using the Legendre numbers. From these the associated Legendre polynomials are obtained and the derivatives of these polynomials at x=0 are derived by using properties of the Legendre numbers.
Paul W. Haggard
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International Journal of Mathematics and Mathematical Sciences, 1985 The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series
Paul W. Haggard
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Radii problems for some classes of analytic functions associated with Legendre polynomials of odd degree [PDF]
Journal of Inequalities and Applications, 2020 The aim of the present paper is to study radii problems for two general classes including various known subclasses of analytic functions associated with the normalized form of Legendre polynomials of odd degree.
Ali Ebadian +4 more
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