Hard Integral of Legendre polynomials
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I can not think of anything with the solution integral, help me, please:
$$ int_{-1}^1 P_n(z) (z^7 + z) dz $$, where $ P_n $- Legendre polynomials.
functional-analysis
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I can not think of anything with the solution integral, help me, please:
$$ int_{-1}^1 P_n(z) (z^7 + z) dz $$, where $ P_n $- Legendre polynomials.
functional-analysis
Well, if $;n;$ is even then the integral is zero...
– DonAntonio
Nov 16 at 16:57
Is $l=1$ or variable?
– gammatester
Nov 16 at 16:59
@gammatester edited
– Павел Якимов
Nov 16 at 17:04
1
Hint: Express $z^7$ and $z$ as a sum of Legendre polynomials (see e.g. Abramowitz/Stegun Table 22.9) and use the orthogonality relations.
– gammatester
Nov 16 at 17:12
1
And if $nge8$ it's zero too
– Richard Martin
Nov 16 at 17:14
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I can not think of anything with the solution integral, help me, please:
$$ int_{-1}^1 P_n(z) (z^7 + z) dz $$, where $ P_n $- Legendre polynomials.
functional-analysis
I can not think of anything with the solution integral, help me, please:
$$ int_{-1}^1 P_n(z) (z^7 + z) dz $$, where $ P_n $- Legendre polynomials.
functional-analysis
functional-analysis
edited Nov 16 at 17:04
asked Nov 16 at 16:43
Павел Якимов
447
447
Well, if $;n;$ is even then the integral is zero...
– DonAntonio
Nov 16 at 16:57
Is $l=1$ or variable?
– gammatester
Nov 16 at 16:59
@gammatester edited
– Павел Якимов
Nov 16 at 17:04
1
Hint: Express $z^7$ and $z$ as a sum of Legendre polynomials (see e.g. Abramowitz/Stegun Table 22.9) and use the orthogonality relations.
– gammatester
Nov 16 at 17:12
1
And if $nge8$ it's zero too
– Richard Martin
Nov 16 at 17:14
add a comment |
Well, if $;n;$ is even then the integral is zero...
– DonAntonio
Nov 16 at 16:57
Is $l=1$ or variable?
– gammatester
Nov 16 at 16:59
@gammatester edited
– Павел Якимов
Nov 16 at 17:04
1
Hint: Express $z^7$ and $z$ as a sum of Legendre polynomials (see e.g. Abramowitz/Stegun Table 22.9) and use the orthogonality relations.
– gammatester
Nov 16 at 17:12
1
And if $nge8$ it's zero too
– Richard Martin
Nov 16 at 17:14
Well, if $;n;$ is even then the integral is zero...
– DonAntonio
Nov 16 at 16:57
Well, if $;n;$ is even then the integral is zero...
– DonAntonio
Nov 16 at 16:57
Is $l=1$ or variable?
– gammatester
Nov 16 at 16:59
Is $l=1$ or variable?
– gammatester
Nov 16 at 16:59
@gammatester edited
– Павел Якимов
Nov 16 at 17:04
@gammatester edited
– Павел Якимов
Nov 16 at 17:04
1
1
Hint: Express $z^7$ and $z$ as a sum of Legendre polynomials (see e.g. Abramowitz/Stegun Table 22.9) and use the orthogonality relations.
– gammatester
Nov 16 at 17:12
Hint: Express $z^7$ and $z$ as a sum of Legendre polynomials (see e.g. Abramowitz/Stegun Table 22.9) and use the orthogonality relations.
– gammatester
Nov 16 at 17:12
1
1
And if $nge8$ it's zero too
– Richard Martin
Nov 16 at 17:14
And if $nge8$ it's zero too
– Richard Martin
Nov 16 at 17:14
add a comment |
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Well, if $;n;$ is even then the integral is zero...
– DonAntonio
Nov 16 at 16:57
Is $l=1$ or variable?
– gammatester
Nov 16 at 16:59
@gammatester edited
– Павел Якимов
Nov 16 at 17:04
1
Hint: Express $z^7$ and $z$ as a sum of Legendre polynomials (see e.g. Abramowitz/Stegun Table 22.9) and use the orthogonality relations.
– gammatester
Nov 16 at 17:12
1
And if $nge8$ it's zero too
– Richard Martin
Nov 16 at 17:14