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QuestionLegendre Polynomial Roots [Solved] Pin
Skippums13-Jan-10 9:56
Skippums13-Jan-10 9:56 
I am attempting to symbolically determine the roots of the 6th and 7th order Legendre polynomials. I started this task by tackling the 6th order polynomial as follows:
P6 = 1/16 * (231x^6 - 315x^4 + 105x^2 - 5)

I first started solving this equation by substituting u=x^2 and went down the path of solving the resulting cubic equation for u, then taking the square root to convert the solution back to x. The first solution I came up with was:
±√[2/33 * (120 - ∛{-15/7 * [751323 - 11√(-3442911)]} - ∛{-15/7 * [751323 + 11√(-3442911)]})]

However, this equation yields the value 0.23982861022165, but the known good value is 0.238619186083197[^]

I tested the result I am getting using the calculator found here[^], and got the same result as my symbolic solution above (be sure to take the square root of the result to convert back to values of x instead of u). Does anyone know why I am coming up with the wrong answer here? I would really appreciate some assistance, as I have grown tired of staring at my solution, searching for the problem. Thanks,

Sounds like somebody's got a case of the Mondays

-Jeff

modified on Wednesday, January 13, 2010 4:32 PM

AnswerRe: Legendre Polynomial Roots Pin
Skippums13-Jan-10 10:32
Skippums13-Jan-10 10:32 
GeneralRe: Legendre Polynomial Roots Pin
harold aptroot13-Jan-10 11:11
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QuestionRe: Legendre Polynomial Roots Pin
Skippums14-Jan-10 9:44
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AnswerRe: Legendre Polynomial Roots Pin
harold aptroot14-Jan-10 10:17
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AnswerRe: Legendre Polynomial Roots Pin
ProtoBytes26-Jan-10 13:41
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Questionselect problem? Pin
miss YY12-Jan-10 20:50
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Tim Craig12-Jan-10 21:27
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QuestionHow to check if a tree is AVL tree? Pin
Cowork8-Jan-10 21:56
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QuestionComplexity help please! Pin
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QuestionRomanization of Japanese using the Hepburn (or related - like ISO_3602) algorithm Pin
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AnswerRe: Romanization of Japanese using the Hepburn (or related - like ISO_3602) algorithm Pin
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QuestionSnake game problem Pin
venomation28-Dec-09 11:03
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AnswerRe: Snake game problem [modified] Pin
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