Question

How to show orthogonality of the Laguerre polynomial $P_n(x)$?

score 209 · Answer 1 · 2020-11-15 11:03:52

209

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How to show orthogonality of the Laguerre polynomial $P_n(x)$?

Published on 15 Nov 2020 - 11:03

score 209 · Answer 2 · 2020-11-17 13:42:06

209

Views

Orthogonal polynomials with respect to $e^{-|x|} \mathrm{d} x$ on the entire real line?

Published on 17 Nov 2020 - 13:42

score 216 · Answer 3 · 2020-11-20 15:05:55

216

Views

Approximate a positive Schwartz function

Published on 20 Nov 2020 - 15:05

score 120 · Answer 4 · 2020-11-23 16:00:12

120

Views

Is the $L^1$-norm of the FT of $(x+i)^n/(x-i)^{n+2}$ bounded as a sequence in $n$?

Published on 23 Nov 2020 - 16:00

score 2.5k · Answer 5 · 2020-12-22 22:05:56

2.5k

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Derive Rodrigues’ formula for Laguerre polynomials

Published on 22 Dec 2020 - 22:05

score 67 · Answer 6 · 2021-01-02 11:11:46

67

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Find $\int\limits_0^\infty {x{e^{ - (a{x^2} + b)}}{I_0}\left( {\sqrt {c{x^2} + dx + k} } \right)dx} $?

Published on 02 Jan 2021 - 11:11

score 45 · Answer 7 · 2021-01-03 23:48:52

45

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Is Rodriguez's representation of the Laguerre polynomials defined $L_n^k(x)= \frac{e^xx^{-k}}{n!}\frac{d^n}{dx^n}(e^{-x}x^{n+k})$?

Published on 03 Jan 2021 - 23:48

score 190 · Answer 8 · 2021-01-04 11:30:15

190

Views

How is the Rodrigues formula $L_n^k(x)=\frac{e^x x^{-k}}{n!}\frac{d^n}{dx^n}(e^{-x}x^{n+k})$ derived?

Published on 04 Jan 2021 - 11:30

score 496 · Answer 9 · 2021-01-04 11:55:39

496

Views

How to modified the Gauss–Laguerre quadrature in the case of $\int\limits_{x=0}^{+\infty}{{e^{-ax}}f(x)}dx$?

Published on 04 Jan 2021 - 11:55

score 353 · Answer 10 · 2021-01-19 00:43:58

353

Views

Prove $\int_0^\infty e^{-x} x^k [L^k_n (x)]^2 \, dx=\frac{(n+k)!}{n!}$

Published on 19 Jan 2021 - 0:43

score 269 · Answer 11 · 2021-01-26 09:41:19

269

Views

Is the sum of the first N Laguerre polynomials (with alternating signs) always positive?

Published on 26 Jan 2021 - 9:41

score 67 · Answer 12 · 2021-02-02 22:32:06

67

Views

A modification of the Laguerre product expansion

Published on 02 Feb 2021 - 22:32

score 119 · Answer 13 · 2021-02-06 20:11:30

119

Views

Sum over (squares of) Laguerre Polynomials

Published on 06 Feb 2021 - 20:11

score 859 · Answer 14 · 2021-02-06 22:10:10

859

Views

Proving that the Laguerre polynomials do indeed solve the differential equation

Published on 06 Feb 2021 - 22:10

score 215 · Answer 15 · 2021-03-12 02:47:14

215

Views

An Integral Equation for the Square of a Laguerre Polynomial

Published on 12 Mar 2021 - 2:47

List Question

How to show orthogonality of the Laguerre polynomial $P_n(x)$?

Orthogonal polynomials with respect to $e^{-|x|} \mathrm{d} x$ on the entire real line?

Approximate a positive Schwartz function

Is the $L^1$-norm of the FT of $(x+i)^n/(x-i)^{n+2}$ bounded as a sequence in $n$?

Derive Rodrigues’ formula for Laguerre polynomials

Find $\int\limits_0^\infty {x{e^{ - (a{x^2} + b)}}{I_0}\left( {\sqrt {c{x^2} + dx + k} } \right)dx} $?

Is Rodriguez's representation of the Laguerre polynomials defined $L_n^k(x)= \frac{e^xx^{-k}}{n!}\frac{d^n}{dx^n}(e^{-x}x^{n+k})$?

How is the Rodrigues formula $L_n^k(x)=\frac{e^x x^{-k}}{n!}\frac{d^n}{dx^n}(e^{-x}x^{n+k})$ derived?

How to modified the Gauss–Laguerre quadrature in the case of $\int\limits_{x=0}^{+\infty}{{e^{-ax}}f(x)}dx$?

Prove $\int_0^\infty e^{-x} x^k [L^k_n (x)]^2 \, dx=\frac{(n+k)!}{n!}$

Is the sum of the first N Laguerre polynomials (with alternating signs) always positive?

A modification of the Laguerre product expansion

Sum over (squares of) Laguerre Polynomials

Proving that the Laguerre polynomials do indeed solve the differential equation

An Integral Equation for the Square of a Laguerre Polynomial

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