| Author(s): K.S. Kölbig | Library: MATHLIB |
| Submitter: | Submitted: 15.02.1989 |
| Language: Fortran | Revised: 01.12.1994 |
Function subprograms RFCONC and DFCONC calculate the (real valued) conical function of the first kind
for real 
, and m=0,1, where 
is the
Legendre (or spherical) function of the first kind and 
.
On CDC and Cray computers, the double-precision version DFCONC is not available.
Structure:
FUNCTION subprograms
User Entry Names: RFCONC, DFCONC
Obsolete User Entry Names: FCONC 
RFCONC
Files Referenced: Unit 6
External References:
| CGAMMA, | WGAMMA, | CLGAMA, | WLGAMA, |
| BESJO, | DBESJ0, | BESJ1, | DBESJ1, |
| BESIO, | DBESI0, | BESI1, | DBESI1, |
| RELIKC, | DELIKC, | RELIEC, | DELIEC, |
| MTLMTR, ABEND | |||
Usage:
For 
(type REAL), 
(type
DOUBLE PRECISION),
tFCONC(X,TAU,M)}has, in any arithmetic expression, the value
.
.
or 
.
Method:
Either (i) series expansions based on the Gaussian
hypergeometric function and evaluated by direct summation
or from rational approximations, or (ii) asymptotic
expressions in terms of Bessel functions. For 
the
conical functions (for m = 0,1) can be expressed in terms of
complete elliptic integrals.
For details see Ref. 1.
Restrictions:
, 
, 
or 1.
Accuracy:
RFCONC (except on CDC and Cray computers)
has full single-precision accuracy.
For most values of the argument X, DFCONC
(and RFCONC on CDC and Cray computers), an accuracy of
not less than 10 significant digits is usually obtained.
If x and 
are not too large
the accuracy increases to about 12-13 significant digits.
Error handling:
Error C331.1: 
or 
or
and 
.
Error C331.2: Problems of convergence for a hypergeometric
function.
In both cases, the function value is set equal to zero,
and a message is written on
Unit 6, unless subroutine MTLSET (N002) has been called.
Notes:
This program is an (only formally) modified version of the CPC Program Library Package FCONIC (see Ref. 1).
References:
for m=0
and m=1, Computer Phys. Comm. 23 (1981) 51-61.
,
(Pergamon Press, Oxford 1966).
