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- #| -*-Scheme-*-
- Copyright (C) 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994,
- 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
- 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Massachusetts
- Institute of Technology
- This file is part of MIT/GNU Scheme.
- MIT/GNU Scheme is free software; you can redistribute it and/or modify
- it under the terms of the GNU General Public License as published by
- the Free Software Foundation; either version 2 of the License, or (at
- your option) any later version.
- MIT/GNU Scheme is distributed in the hope that it will be useful, but
- WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- General Public License for more details.
- You should have received a copy of the GNU General Public License
- along with MIT/GNU Scheme; if not, write to the Free Software
- Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
- USA.
- |#
- ;;; LEGENDRE.SCM -- the Legendre Polynomials returned as a stream or singly
- ;;; Edited by GJS 10Jan09
- (declare (usual-integrations))
- ;;; The following defines a stream whose nth term (0-based) is
- ;;; P[n]. We use the recurrence relation:
- ;;; P[0](x) = 1, P[1](x) = x
- ;;; and for n > 1
- ;;; P[n](x) = ((2n-1)/n)*x*P[n-1](x) - ((n-1)/n)*P[n-2](x)
- (define legendre-polynomials
- (cons-stream poly:one
- (cons-stream poly:identity
- (map-streams (lambda (p1 p2)
- (let* ((n (+ (poly:degree p1) 1))
- (a (/ (- (* 2 n) 1) n))
- (b (/ (- n 1) n)))
- (poly:- (poly:* (poly:scale poly:identity a) p1)
- (poly:scale p2 b))))
- (tail legendre-polynomials)
- legendre-polynomials))))
- (define (legendre-polynomial n)
- (stream-ref legendre-polynomials n))
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