ABRAM
Name:
Type:
Purpose:
Compute the Abramowitz function.
Description:
The Abramowitz function is defined as:
\[ f_{m}(x) = \int_{0}^{\infty}
{t^{m}e^{{t^{2}  \frac{x}{t}}} dt}
\hspace{0.2 in} x \ge 0 \]
where the integral is defined from 0 to positive infinity and
\( m \), a nonnegative integer, is the order of the Abramowitz
function. Dataplot supports values of \( m \) from 0 to 100.
For \( m \) > 2, the following recurrence formula is used:
\[ 2 f_{m}(x) = (m1) f_{m2}(x) + x f_{m3}(x) \]
Dataplot computes this function using ACM Algorithm 757 (see
Reference: below).
Syntax:
LET <y> = ABRAM(<x>,<ord>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a nonnegative number, variable or parameter;
<ord> is a nonnegative integer number, parameter, or
variable in the range 0 to 100;
<y> is a variable or a parameter (depending on what
<x> and <ord> are) where the computed
Abramowitz function values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = ABRAM(2.3,1)
LET A = ABRAM(X,A1)
LET X2 = ABRAM(X1,4) FOR X1 = 0.1 0.1 3.0
Note:
Library functions are distinguished from let subcommands
in the following ways.
 Functions enclose the input value in parenthesis. Let
subcommands use spaces.
 Functions can accept (and return) either parameters
(i.e., single values) or variables (i.e., an array of
values) while let subcommands are specific in which they
accept as input and what they return as output.
 Functions can accept expressions while let subcommands
do not. For example, the following is legal:
For let subcommands, you typically have to do something
like the following:
LET YTEMP = Y**2 + 8
LET A = SUM YTEMP
Default:
Synonyms:
Related Commands:
CLAUSN

=

Compute the Clausen integral.

DEBEYE

=

Compute the Debeye function.

EXP3

=

Compute the cubic exponential integral.

GOODST

=

Compute the Goodwin and Stanton integral.

LOBACH

=

Compute the Lobachevski integral.

SYNCH1

=

Compute the synchrotron radiation function.

SYNCH2

=

Compute the synchrotron radiation function.

STROM

=

Compute the Stromgren integral.

TRAN

=

Compute the transport integral.

Reference:
Allan MacLead (1996), "ACM Transactions of Mathematical Software,"
Vol. 22, No. 3, pp. 288301.
Applications:
Implementation Date:
Program:
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 5 5 95 95
YLIMITS 0 1
TITLE ORDER 0
PLOT ABRAM(X,0) FOR X = 0 0.01 5
TITLE ORDER 1
PLOT ABRAM(X,1) FOR X = 0 0.01 5
TITLE ORDER 2
PLOT ABRAM(X,2) FOR X = 0 0.01 5
TITLE ORDER 3
PLOT ABRAM(X,3) FOR X = 0 0.01 5
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT ABRAMOWITZ FUNCTIONS
