************80
! CHGU computes the confluent hypergeometric function U(a,b,x).
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:
27 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, real ( kind = 8 ) A, B, parameters.
Input, real ( kind = 8 ) X, the argument.
Output, real ( kind = 8 ) HU, U(a,b,x).
Output, integer ( kind = 4 ) MD, the method code.
Type | Intent | Optional | Attributes | Name | ||
---|---|---|---|---|---|---|
real(kind=8) | :: | a | ||||
real(kind=8) | :: | b | ||||
real(kind=8) | :: | x | ||||
real(kind=8) | :: | hu | ||||
integer(kind=4) | :: | md |
subroutine chgu ( a, b, x, hu, md ) !*****************************************************************************80 ! !! CHGU computes the confluent hypergeometric function U(a,b,x). ! ! 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: ! ! 27 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, real ( kind = 8 ) A, B, parameters. ! ! Input, real ( kind = 8 ) X, the argument. ! ! Output, real ( kind = 8 ) HU, U(a,b,x). ! ! Output, integer ( kind = 4 ) MD, the method code. ! implicit none real ( kind = 8 ) a real ( kind = 8 ) a00 real ( kind = 8 ) aa real ( kind = 8 ) b real ( kind = 8 ) b00 logical bl1 logical bl2 logical bl3 logical bn real ( kind = 8 ) hu real ( kind = 8 ) hu1 integer ( kind = 4 ) id integer ( kind = 4 ) id1 logical il1 logical il2 logical il3 integer ( kind = 4 ) md real ( kind = 8 ) x aa = a - b + 1.0D+00 il1 = a == int ( a ) .and. a <= 0.0D+00 il2 = aa == int ( aa ) .and. aa <= 0.0D+00 il3 = abs ( a * ( a - b + 1.0D+00 ) ) / x <= 2.0D+00 bl1 = x <= 5.0D+00 .or. ( x <= 10.0D+00 .and. a <= 2.0D+00 ) bl2 = ( 5.0D+00 < x .and. x <= 12.5D+00 ) .and. & ( 1.0D+00 <= a .and. a + 4.0D+00 <= b ) bl3 = 12.5D+00 < x .and. 5.0D+00 <= a .and. a + 5.0D+00 <= b bn = b == int ( b ) .and. b .ne. 0.0D+00 id1 = -100 if ( b .ne. int ( b ) ) then call chgus ( a, b, x, hu, id1 ) md = 1 if ( 6 <= id1 ) then return end if hu1 = hu end if if ( il1 .or. il2 .or. il3 ) then call chgul ( a, b, x, hu, id ) md = 2 if ( 6 <= id ) then return end if if ( id < id1 ) then md = 1 id = id1 hu = hu1 end if end if if ( 0.0D+00 <= a ) then if ( bn .and. ( bl1 .or. bl2 .or. bl3 ) ) then call chgubi ( a, b, x, hu, id ) md = 3 else call chguit ( a, b, x, hu, id ) md = 4 end if else if ( b <= a ) then a00 = a b00 = b a = a - b + 1.0D+00 b = 2.0D+00 - b call chguit ( a, b, x, hu, id ) hu = x ** ( 1.0D+00 - b00 ) * hu a = a00 b = b00 md = 4 else if ( bn .and. ( .not. il1 ) ) then call chgubi ( a, b, x, hu, id ) md = 3 end if end if if ( id < 6 ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'CHGU - Warning!' write ( *, '(a)' ) ' Accurate results were not obtained.' end if return end subroutine chgu