Question

Find closed-form Infinite summation of two Legendre polynomials's product

score 83 · Answer 1 · 2017-05-21 09:27:17

83

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Find closed-form Infinite summation of two Legendre polynomials's product

Published on 21 May 2017 - 9:27

score 108 · Answer 2 · 2017-05-24 03:20:58

108

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Value of $\sum^{n+1}_{k=0}{n+1 \choose k}^2p^k-\sum^{n}_{k=0}{n \choose k}^2p^k$?

Published on 24 May 2017 - 3:20

score 153 · Answer 3 · 2017-05-31 01:32:37

153

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Equivalent expression for $n\sum^n_{k=0}{n\choose k}^2a^{n-k}b^k-(n-1)\sum^{n-1}_{k=0}{n-1\choose k}^2a^{n-1-k}b^k$

Published on 31 May 2017 - 1:32

score 245 · Answer 4 · 2017-05-31 04:48:03

245

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Getting a base of polynomials on [a,b] from a base of Legendre polynomials (orthogonal on [-1,1])

Published on 31 May 2017 - 4:48

score 217 · Answer 5 · 2017-06-01 14:47:47

217

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Double summation over a product of combinations

Published on 01 Jun 2017 - 14:47

score 49 · Answer 6 · 2017-06-06 00:06:03

49

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Clarifycation on an expression involving the derivative of a Legendre Polynomial

Published on 06 Jun 2017 - 0:06

score 806 · Answer 7 · 2017-06-11 08:15:14

806

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Convergence of Series involving Legendre Polynomials

Published on 11 Jun 2017 - 8:15

score 228 · Answer 8 · 2026-03-25 16:02:03

228

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How to calculate the mean and the variance for the function with Multidimensional Polynomial Chaos Approach?

Published on 25 Mar 2026 - 16:02

score 620 · Answer 9 · 2017-06-16 17:20:39

620

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Integration of Legendre Polynomials with different arguments

Published on 16 Jun 2017 - 17:20

score 6.2k · Answer 10 · 2017-06-19 03:26:53

6.2k

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Showing orthogonality of Legendre polynomials using Rodrigues' formula

Published on 19 Jun 2017 - 3:26

score 1.4k · Answer 11 · 2017-07-06 09:55:03

1.4k

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Are $1-x^2$ and $-2x$ analytical functions?

Published on 06 Jul 2017 - 9:55

score 498 · Answer 12 · 2017-07-08 17:16:21

498

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Hypergeometric relation from Legendre functions

Published on 08 Jul 2017 - 17:16

score 163 · Answer 13 · 2017-07-16 09:22:29

163

Views

How to calculate $\int_{-1}^{1} \left( \frac{1}{2^nn!}\frac{d^n}{dx^n}\left(x^2-1\right)^n \left(x\right)\right)^2dx$?

Published on 16 Jul 2017 - 9:22

score 5.2k · Answer 14 · 2017-07-20 07:35:22

5.2k

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Solving Legendre's Differential Equation

Published on 20 Jul 2017 - 7:35

score 415 · Answer 15 · 2017-07-24 15:50:46

415

Views

Recursions for Legendre polynomials of the second kind on the interval [1, inf)

Published on 24 Jul 2017 - 15:50

List Question

Find closed-form Infinite summation of two Legendre polynomials's product

Value of $\sum^{n+1}_{k=0}{n+1 \choose k}^2p^k-\sum^{n}_{k=0}{n \choose k}^2p^k$?

Equivalent expression for $n\sum^n_{k=0}{n\choose k}^2a^{n-k}b^k-(n-1)\sum^{n-1}_{k=0}{n-1\choose k}^2a^{n-1-k}b^k$

Getting a base of polynomials on [a,b] from a base of Legendre polynomials (orthogonal on [-1,1])

Double summation over a product of combinations

Clarifycation on an expression involving the derivative of a Legendre Polynomial

Convergence of Series involving Legendre Polynomials

How to calculate the mean and the variance for the function with Multidimensional Polynomial Chaos Approach?

Integration of Legendre Polynomials with different arguments

Showing orthogonality of Legendre polynomials using Rodrigues' formula

Are $1-x^2$ and $-2x$ analytical functions?

Hypergeometric relation from Legendre functions

How to calculate $\int_{-1}^{1} \left( \frac{1}{2^nn!}\frac{d^n}{dx^n}\left(x^2-1\right)^n \left(x\right)\right)^2dx$?

Solving Legendre's Differential Equation

Recursions for Legendre polynomials of the second kind on the interval [1, inf)

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