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! LEGZO computes the zeros of Legendre polynomials, and integration weights.
Discussion:
This procedure computes the zeros of Legendre polynomial Pn(x) in the
interval [-1,1], and the corresponding weighting coefficients for
Gauss-Legendre integration.
Licensing:
This routine is copyrighted by Shanjie Zhang and Jianming Jin. However,
they give permission to incorporate this routine into a user program
provided that the copyright is acknowledged.
Modified:
13 July 2012
Author:
Shanjie Zhang, Jianming Jin
Reference:
Shanjie Zhang, Jianming Jin,
Computation of Special Functions,
Wiley, 1996,
ISBN: 0-471-11963-6,
LC: QA351.C45.
Parameters:
Input, integer ( kind = 4 ) N, the order of the polynomial.
Output, real ( kind = 8 ) X(N), W(N), the zeros of the polynomial,
and the corresponding weights.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer(kind=4) | :: | n | ||||
| real(kind=8) | :: | x(n) | ||||
| real(kind=8) | :: | w(n) |