Question

Inner Product of Chebyshev polynomials of the second kind with $x$ as weighting

score 647 · Answer 1 · 2016-02-04 19:15:52

647

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Inner Product of Chebyshev polynomials of the second kind with $x$ as weighting

Published on 04 Feb 2016 - 19:15

score 410 · Answer 2 · 2016-02-09 01:21:36

410

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How can I show that this Jacobi polynomial can be expressed as the sum of these two Legendre polynomials?

Published on 09 Feb 2016 - 1:21

score 183 · Answer 3 · 2016-02-11 21:09:43

183

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Refences to Sturm–Liouville theory with a singular weight function.

Published on 11 Feb 2016 - 21:09

score 317 · Answer 4 · 2016-02-19 23:06:56

317

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Orthogonality relation as double sum of products of binomial coefficients

Published on 19 Feb 2016 - 23:06

score 132 · Answer 5 · 2016-02-21 13:22:38

132

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Expansion of some singular kernel with the help of Bessel and Neumann spherical harmonic functions

Published on 21 Feb 2016 - 13:22

score 31 · Answer 6 · 2016-03-02 02:57:40

31

Views

Monte Carlo integration to solve coefficients of an orthogonal series - reusing the set of random points

Published on 02 Mar 2016 - 2:57

score 137 · Answer 7 · 2016-03-05 22:35:34

137

Views

Orthogonal polynomial and inner products problem

Published on 05 Mar 2016 - 22:35

score 6k · Answer 8 · 2016-03-06 23:56:04

6k

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Deriving Hermite polynomial derivative recurrence relation straight from differential equation.

Published on 06 Mar 2016 - 23:56

score 2.8k · Answer 9 · 2016-03-13 15:15:19

2.8k

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Orthogonal Projection of a function

Published on 13 Mar 2016 - 15:15

score 135 · Answer 10 · 2016-03-19 16:20:23

135

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The Meaning of the Orthogonal Projection Transformation

Published on 19 Mar 2016 - 16:20

score 95 · Answer 11 · 2016-03-21 22:33:16

95

Views

Simplify Legendre Polynomial times a power

Published on 21 Mar 2016 - 22:33

score 505 · Answer 12 · 2016-03-28 21:40:43

505

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Solution to Systems of Equations, Orthogonal Polynomials

Published on 28 Mar 2016 - 21:40

score 14.2k · Answer 13 · 2016-04-03 01:21:54

14.2k

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Show the Integration of Legendre Polynomials is 0

Published on 03 Apr 2016 - 1:21

score 104 · Answer 14 · 2016-04-06 21:30:48

104

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Prove that $\int_1^{\frac{1+z}{1-z}} \frac{d^n}{dz^n} (z^2-1)^n= -\frac{2(z-1)^n}{(n+1)! }\frac{d^n}{dz^n} (\frac{z}{z-1})^{n+1} $

Published on 06 Apr 2016 - 21:30

score 113 · Answer 15 · 2016-04-13 20:56:28

113

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Understanding part of the proof that $\int_{x=-1}^1P_L(x)P_M(x)\,\rm{d} x =0\quad\text{(for}\,\, L\ne M)$

Published on 13 Apr 2016 - 20:56

List Question

Inner Product of Chebyshev polynomials of the second kind with $x$ as weighting

How can I show that this Jacobi polynomial can be expressed as the sum of these two Legendre polynomials?

Refences to Sturm–Liouville theory with a singular weight function.

Orthogonality relation as double sum of products of binomial coefficients

Expansion of some singular kernel with the help of Bessel and Neumann spherical harmonic functions

Monte Carlo integration to solve coefficients of an orthogonal series - reusing the set of random points

Orthogonal polynomial and inner products problem

Deriving Hermite polynomial derivative recurrence relation straight from differential equation.

Orthogonal Projection of a function

The Meaning of the Orthogonal Projection Transformation

Simplify Legendre Polynomial times a power

Solution to Systems of Equations, Orthogonal Polynomials

Show the Integration of Legendre Polynomials is 0

Prove that $\int_1^{\frac{1+z}{1-z}} \frac{d^n}{dz^n} (z^2-1)^n= -\frac{2(z-1)^n}{(n+1)! }\frac{d^n}{dz^n} (\frac{z}{z-1})^{n+1} $

Understanding part of the proof that $\int_{x=-1}^1P_L(x)P_M(x)\,\rm{d} x =0\quad\text{(for}\,\, L\ne M)$

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