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*DECK ALPLGN
DOUBLE PRECISION FUNCTION ALPLGN(L,M,X)
*
*-----------------------------------------------------------------------
*
*Purpose:
* return the Ferrer definition of the associated Legendre function.
*
*Copyright:
* Copyright (C) 2021 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* L main index
* M secondary index
* X direction cosine
*
*-----------------------------------------------------------------------
*
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
INTEGER L,M
DOUBLE PRECISION X
INTEGER, ALLOCATABLE, DIMENSION(:) :: IPX
*
IF(M.LT.0) THEN
CALL XABORT('ALPLGN: BAD ARGUMENTS (1)')
ELSE IF(M.GT.L) THEN
CALL XABORT('ALPLGN: BAD ARGUMENTS (2)')
ELSE IF(ABS(X).GT.1.0D0) THEN
CALL XABORT('ALPLGN: BAD ARGUMENTS (3)')
ENDIF
PMM=1.0D0
IF(M.GT.0) THEN
ALLOCATE(IPX(2*M))
DO I=1,2*M
IPX(I)=I
ENDDO
PMM=PRODUCT(IPX,MASK=MOD(IPX,2)==1)*SQRT((1.0D0-X)*(1.0D0+X))**M
DEALLOCATE(IPX)
ENDIF
IF(L.EQ.M) THEN
ALPLGN=PMM
ELSE
PMMP1=(2*M+1)*X*PMM
IF(L.EQ.M+1) THEN
ALPLGN=PMMP1
ELSE
PLL=0.0D0
DO LL=M+2,L
PLL=((2*LL-1)*X*PMMP1-(LL+M-1)*PMM)/(LL-M)
PMM=PMMP1
PMMP1=PLL
ENDDO
ALPLGN=PLL
ENDIF
ENDIF
RETURN
END
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