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Laguerre polynomials with integration over entire axis

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#orthogonal-polynomials #laguerre-polynomials
85
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about the Laguerre square expansion Sin(x)

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#calculus #laguerre-polynomials
136
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Double series with Beta reciprocals $\sum_{j=0}^\infty \sum_{k=0}^\infty \frac{x^j}{j!}\frac{y^k}{k!} \frac{1}{\boldsymbol{B}(j+1,k+1)} = ? $

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#sequences-and-series #gamma-function #beta-function #laguerre-polynomials
165
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Generating function of the Confluent Hypergeometric Function of the First Kind

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#sequences-and-series #hypergeometric-function #laguerre-polynomials
123
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Integration of Gaussian $\times$ Laguerre functions

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#integration #definite-integrals #gaussian-integral #laguerre-polynomials
30
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The Correct Change of Variable of an nth Order Derivative

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#real-analysis #derivatives #polynomials #change-of-variable #laguerre-polynomials
109
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How should I prove $\int_0^\infty\frac{d^j}{dx^j}(x^je^{-x})dx=0$?

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#integration #solution-verification #inner-products #orthogonality #laguerre-polynomials
156
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How to modified the Gauss–Laguerre quadrature in the case of $\int\limits_{10}^{\infty}{{e^{-x}}f(x)}\mathrm{d}x$?

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#integration #numerical-methods #laguerre-polynomials
103
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Alternative roots of generalized Laguerre polynomials

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#roots #stirling-numbers #laguerre-polynomials
101
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Fractional Laguerre function $L_{n-\frac{1}{2}}(x)$

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#calculus #polynomials #bessel-functions #fractional-calculus #laguerre-polynomials
40
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Searching for weighted-$L^1$ summable orthonormal basis of $L^2(0,\infty)$

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#orthonormal #change-of-basis #chebyshev-polynomials #hermite-polynomials #laguerre-polynomials
46
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How to evaluate directly Associated Laguerre Polynomial multiplied with $e^{-x/2} x^{k/2}$?

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#special-functions #laguerre-polynomials
63
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Integral involving Bessel functions, exponential and two Laguerre polynomials

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#definite-integrals #physics #bessel-functions #laguerre-polynomials
309
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Addition formula for generalized Laguerre polynomials

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#special-functions #generating-functions #orthogonal-polynomials #hermite-polynomials #laguerre-polynomials
46
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Find Special Function from Series Form?

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#taylor-expansion #power-series #laguerre-polynomials

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