Integral involving Legendre polynomial [closed]Legendre Polynomial manipulationsDefinite integral involving Legendre PolynomialHow to show that any Legendre polynomial, over $[-1,1]$, is bounded by one in absolute value?Integration of Legendre PolynomialIntegral involving Legendre polynomial and $x^n$Inequality involving Legendre polynomialsShifted Legendre PolynomialIntegral involving Legendre polynomialsLegendre Polynomial Orthogonality IntegralDefinite Integral in Legendre polynomial formula

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Integral involving Legendre polynomial [closed]


Legendre Polynomial manipulationsDefinite integral involving Legendre PolynomialHow to show that any Legendre polynomial, over $[-1,1]$, is bounded by one in absolute value?Integration of Legendre PolynomialIntegral involving Legendre polynomial and $x^n$Inequality involving Legendre polynomialsShifted Legendre PolynomialIntegral involving Legendre polynomialsLegendre Polynomial Orthogonality IntegralDefinite Integral in Legendre polynomial formula













-1












$begingroup$


Does anyone know how to prove the following integration?



beginequation
int_-1^1sqrtfrac1-x2 P_n(x) textdx=frac-4(2n-1)(2n+1)(2n+3).
endequation










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New contributor




K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$



closed as off-topic by mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin Mar 13 at 0:23


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin
If this question can be reworded to fit the rules in the help center, please edit the question.











  • 2




    $begingroup$
    Welcome to MSE. Please give some context, in particular, tell us what you've tried so far, including anything in particular you had difficulty with. Also, letting us know where this problem comes from would be helpful. Thanks.
    $endgroup$
    – John Omielan
    Mar 12 at 20:19










  • $begingroup$
    I guessed this formula. It could be right because I tried the first several values. This formula can be used in research about the random walk on the sphere.
    $endgroup$
    – K K
    Mar 13 at 17:13















-1












$begingroup$


Does anyone know how to prove the following integration?



beginequation
int_-1^1sqrtfrac1-x2 P_n(x) textdx=frac-4(2n-1)(2n+1)(2n+3).
endequation










share|cite|improve this question







New contributor




K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$



closed as off-topic by mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin Mar 13 at 0:23


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin
If this question can be reworded to fit the rules in the help center, please edit the question.











  • 2




    $begingroup$
    Welcome to MSE. Please give some context, in particular, tell us what you've tried so far, including anything in particular you had difficulty with. Also, letting us know where this problem comes from would be helpful. Thanks.
    $endgroup$
    – John Omielan
    Mar 12 at 20:19










  • $begingroup$
    I guessed this formula. It could be right because I tried the first several values. This formula can be used in research about the random walk on the sphere.
    $endgroup$
    – K K
    Mar 13 at 17:13













-1












-1








-1





$begingroup$


Does anyone know how to prove the following integration?



beginequation
int_-1^1sqrtfrac1-x2 P_n(x) textdx=frac-4(2n-1)(2n+1)(2n+3).
endequation










share|cite|improve this question







New contributor




K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




Does anyone know how to prove the following integration?



beginequation
int_-1^1sqrtfrac1-x2 P_n(x) textdx=frac-4(2n-1)(2n+1)(2n+3).
endequation







legendre-polynomials






share|cite|improve this question







New contributor




K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







New contributor




K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question






New contributor




K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked Mar 12 at 20:05









K KK K

1




1




New contributor




K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






K K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




closed as off-topic by mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin Mar 13 at 0:23


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin
If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin Mar 13 at 0:23


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mrtaurho, John Omielan, Vinyl_cape_jawa, YiFan, Lee David Chung Lin
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 2




    $begingroup$
    Welcome to MSE. Please give some context, in particular, tell us what you've tried so far, including anything in particular you had difficulty with. Also, letting us know where this problem comes from would be helpful. Thanks.
    $endgroup$
    – John Omielan
    Mar 12 at 20:19










  • $begingroup$
    I guessed this formula. It could be right because I tried the first several values. This formula can be used in research about the random walk on the sphere.
    $endgroup$
    – K K
    Mar 13 at 17:13












  • 2




    $begingroup$
    Welcome to MSE. Please give some context, in particular, tell us what you've tried so far, including anything in particular you had difficulty with. Also, letting us know where this problem comes from would be helpful. Thanks.
    $endgroup$
    – John Omielan
    Mar 12 at 20:19










  • $begingroup$
    I guessed this formula. It could be right because I tried the first several values. This formula can be used in research about the random walk on the sphere.
    $endgroup$
    – K K
    Mar 13 at 17:13







2




2




$begingroup$
Welcome to MSE. Please give some context, in particular, tell us what you've tried so far, including anything in particular you had difficulty with. Also, letting us know where this problem comes from would be helpful. Thanks.
$endgroup$
– John Omielan
Mar 12 at 20:19




$begingroup$
Welcome to MSE. Please give some context, in particular, tell us what you've tried so far, including anything in particular you had difficulty with. Also, letting us know where this problem comes from would be helpful. Thanks.
$endgroup$
– John Omielan
Mar 12 at 20:19












$begingroup$
I guessed this formula. It could be right because I tried the first several values. This formula can be used in research about the random walk on the sphere.
$endgroup$
– K K
Mar 13 at 17:13




$begingroup$
I guessed this formula. It could be right because I tried the first several values. This formula can be used in research about the random walk on the sphere.
$endgroup$
– K K
Mar 13 at 17:13










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