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On Legendre numbers of the second kind [PDF]
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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Problems and methods of calculating the Legendre functions of arbitrary degree and order [PDF]
Geodesy and Cartography, 2016 The known standard recursion methods of computing the full normalized associated Legendre functions do not give the necessary precision due to application of IEEE754-2008 standard, that creates a problems of underflow and overflow.
Novikova Elena, Dmitrenko Alexander
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Some integrals involving associated Legendre functions [PDF]
Mathematics of Computation, 1974 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.
S. N. Samaddar
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Integral of Legendre polynomials and its properties [PDF]
Mathematics and Computational SciencesThis paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
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The generalized associated Legendre functions [PDF]
, 2001 Mathematics Subject Classification: 33C60, 33C20, 44A15This paper is devoted to an important case of Wright’s hypergeometric function 2Fτ,β1(a, b; c; z) = 2Fτ,β1(z), to studying its basic properties and to application of 2Fτ,β1(z) to the generalization ...
Virchenko, Nina, Rumiantseva, Olena
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An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 This study addresses the inverse issue of identifying the space-dependent heat source of the heat equation, which is stated using the optimal con-trol framework.
T. Shojaeizadeh, M. Darehmiraki
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Multi-integral representations for Jacobi functions of the first and second kind
Arab Journal of Basic and Applied Sciences, 2023 One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the degree is allowed to be a complex number instead of a non-negative integer.
Howard S. Cohl, Roberto S. Costas-Santos
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Two New Integral Transforms and Their Applications [PDF]
, 1972 This thesis is in two parts. In Part I the independent variable θ in the trigonometric form of Legendre's equation is extended to the range ( -∞, ∞).
Newhall, X X (Nicholas)
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Stability of Traveling Waves Based upon the Evans Function and Legendre Polynomials
Applied Sciences, 2020 One of the tools and techniques concerned with the stability of nonlinear waves is the Evans function which is an analytic function whose zeros give the eigenvalues of the linearized operator.
H. M. Srivastava +2 more
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Evaluation of hierarchical vector basis functions for quadrilateral cells [PDF]
, 2011 New hierarchical vector basis functions for quadrilateral cells are introduced, and the matrix condition numbers associated with their use are compared to those of existing vector basis families to assess the relative linear independence of the functions.
Peterson A. F. +4 more
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