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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  • 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















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







share|cite|improve this question
























  • 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













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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








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


















  • 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















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