Prove that P2n(0)= (-1)n ((2n-1)!!/(2n)!!) using the generation function and a binomial expansion...

Question

Question

Prove that P_2n(0)= (-1)ⁿ ((2n-1)!!/(2n)!!) using the generation function and a binomial expansion.

Show that (sqrt(pi)(4n-1)/(2gamma(n+1)gamma(3/2-n))=(-1)^n-1((2n-3)!!/(2n-2)!!)(4n-1)/2n

math Advanced-Math

Answer 1

Answer #1

The generating function of Legendre polynomials is Put χ= 0, we get 2 2 4 2 4 6 equating the coeffient of !* both sides, we g

Answer 2

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