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# Numerical Evaluation of Special Functions

**D. W. Lozier and F. W. J. Olver**

** 5.13. Weber Parabolic Cylinder Functions
. **

See also confluent hypergeometric functions (§ 5.5).

5.13.1. * Real Arguments and Parameters. *

Software Packages:

[** Tau92**, Fortran]
.

Intermediate Libraries:

[** Bak92**]
.

5.13.2. * Articles. *

[** LR74**]
,
[** MMV81**]
,
[** RL76**]
,
[** SGA81**]
.

**Bak92**-
L. Baker,
* C mathematical function handbook*, McGraw-Hill, Inc., New
York, 1992, includes diskette.

**LR74**-
W. P. Latham and R. W. Redding,
* On the calculation of the parabolic
cylinder functions*, J. Comput. Phys. ** 16** (1974), 66--75.

**MMV81**-
G. Maino, E. Menapace, and A. Ventura,
* Computation of parabolic cylinder
functions by means of a Tricomi expansion*, J. Comput. Phys. ** 40**
(1981), 294--304.

**RL76**-
R. W. Redding and W. P. Latham,
* On the calculation of the parabolic
cylinder functions. II. The function *, J. Comput. Phys. **
20** (1976), 256--258.

**SGA81**-
Z. Schulten, R. G. Gordon, and D. G. M. Anderson,
* A numerical algorithm
for the evaluation of Weber parabolic cylinder functions , and *, J. Comput. Phys. ** 42** (1981), 213--237.

**Tau92**-
G. Taubmann,
* Parabolic cylinder functions for natural ***n** and
positive **x**, Comput. Phys. Comm. ** 69** (1992), 415--419.

### Abstract:

*This document is an excerpt from the current hypertext version of
an article that appeared in Walter Gautschi (ed.),
** Mathematics of Computation 1943--1993: A Half-Century of
Computational Mathematics*, Proceedings of Symposia in
Applied Mathematics 48, American Mathematical Society,
Providence, RI 02940, 1994.
The symposium was held at the University of British Columbia
August 9--13, 1993, in honor of the fiftieth anniversary of
the journal * Mathematics of Computation*.
The original abstract follows.

*
Higher transcendental functions continue to play varied and
important roles in investigations by engineers, mathematicians,
scientists and statisticians.
The purpose of this paper is to assist in locating useful approximations
and software for the numerical generation of these functions, and to
offer some suggestions for future developments in this field.
*

Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, Md 20899

* E-mail address: dlozier@nist.gov*

Institute for Physical Science and Technology,
University of Maryland,
College Park, MD 20742

* E-mail address: olver@bessel.umd.edu*

The research of the second author has been supported by NSF
Grant CCR 89-14933.

1991 * Mathematics Subject Classification*. Primary 65D20;
Secondary 33-00.

*Daniel W Lozier *

Fri Apr 7 14:25:01 EDT 1995