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15
94
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Integration of a square of Conical (Mehler) function

Published on
#calculus #definite-integrals #special-functions #legendre-polynomials #legendre-functions
78
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Generating function of orthogonal polynomial basis

Published on
#functional-analysis #orthogonal-polynomials #legendre-polynomials #hermite-polynomials
20
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further simplification of a summation involving Legendre and Associated Legendre polynomials

Published on
#power-series #legendre-polynomials
172
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Legendre polynomials: computing $\int_0^1 xP_n(x)\,dx$

Published on
#integration #mathematical-physics #legendre-polynomials
51
Views

Show that $K(u)=\sum_{k=0}^r P_k(0) P_k(u) \mathbf{1}_{\{|u| \leq 1\}}$ is a kernel of order $r$

Published on
#hilbert-spaces #order-statistics #orthogonal-polynomials #legendre-polynomials #reproducing-kernel-hilbert-spaces
99
Views

Showing that a series that involves Legendre polynomial converges.

Published on
#real-analysis #sequences-and-series #power-series #legendre-polynomials
44
Views

partial alternating sum of legendre polynomial

Published on
#special-functions #legendre-polynomials #spherical-harmonics
71
Views

Does it make sense to think about formal power series where the coefficients belong to a Ring?

Published on
#polynomials #ring-theory #legendre-polynomials #formal-power-series
378
Views

Prove that the Legendre polynomials satisfy $P_n(1) = 1$ and $P_n(-1)=(-1)^n$

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#partial-derivative #mathematical-physics #legendre-polynomials
123
Views

Series of product of legendre polynomials with shifted degree

Published on
#power-series #generating-functions #quantum-mechanics #legendre-polynomials #hadamard-product
73
Views

Legendre expansion of a root polynomial

Published on
#fourier-series #legendre-polynomials
36
Views

Proof of an identity of a Gaussian series over Legendre polynomials

Published on
#sequences-and-series #exponential-function #legendre-polynomials
32
Views

Establishing Recurrence Relation for Legendre Polynomials using Rodrigues' Formula

Published on
#recurrence-relations #legendre-polynomials #legendre-functions
77
Views

How do I find the leading coefficient of a Legendre polynomial?

Published on
#orthogonal-polynomials #legendre-polynomials
402
Views

Bivariate generating function for squared binomial coefficients

Published on
#binomial-coefficients #generating-functions #legendre-polynomials

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