Use rodriguess formula to calculate the fifth legendre...

Transcript

00:01 Hello, the question is taken from calculers and the question is use a outreach formula to calculate the fifth legendary polynomial.

00:09 So we need to evaluate p5x by using the orderage formula.

00:14 And the orderage formula is pn x is 1 over 2 to the power n, n factorial, dn over d x to the power n, x square minus 1 to the power n.

00:26 So p 5x will be 1 over 2 to the power 5 5 factorial d 5 over d x 5 into x square minus 1 to the power 5 further solving it we get 1 over 2 to the power 4 is this will be 32 32 into 5 factorial is 5 4 the 20 6 the 120 and d 4 over d x 4 will be 5 into x square minus 1 to the power 4 and 2 x so this will be 1 by 0 32 to the 64 32 and 6 30 so d cube over d cube over the x cube into the taking 10 outside so we get the differentiation of x is 1 so x square minus 1 to the power 4 plus x into 4 x square minus 1 cube into 2x and further this is equal to 1 over 3 8 4 d square over d x square let us differentiating it we get 4 into x square minus 1 cube into 2x plus this is 8 x square so this will be 16 x and x square minus 1 cube plus 8 x square 2 3 into x square minus 1 whole square into 2x so this will give you the value 1 over 3 8 4 d square over the x square let us first manage it so this will be 8 x into x square minus 1 q plus this is 16 x and 8 x 16 and 8 24 so this will be 24 x plus 3 to the 6 8 the 48 x square x square minus 1 whole square so taking 24 common so we get 24 over 3 8 4 d square over d x square into x x square minus 1 whole cube plus x square to x square x square minus 1 whole square okay so 3 8 the 24 3 1, 3 to the 6, 3 at the 24, 4 to the 8.

03:12 4 to the 8.

03:15 So this will be 1 by 16.

03:19 And d over dx, again differentiating, we get x -square minus 1 cube plus 3x into x square minus 1 whole square into 2x plus 4x into x square minus 1 whole square plus 2x2x2...

Question

Use Rodrigues's formula to calculate the fifth Legendre polynomial P₅(x).

Question

Use Rodrigues's formula to calculate the fifth Legendre polynomial P₅(x).

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