ABRAM

ABRAM (LET)

Library Function

Compute the Abramowitz function.

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 non-negative 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:

\[ 2 f_{m}(x) = (m-1) f_{m-2}(x) + x f_{m-3}(x) \]

Dataplot computes this function using ACM Algorithm 757 (see Reference: below).

LET <y> = ABRAM(<x>,<ord>) <SUBSET/EXCEPT/FOR qualification>
where <x> is a non-negative number, variable or parameter;
          <ord> is a non-negative 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.

LET A = ABRAM(2.3,1)
LET A = ABRAM(X,A1)
LET X2 = ABRAM(X1,4) FOR X1 = 0.1 0.1 3.0

Library functions are distinguished from let subcommands in the following ways.
1. Functions enclose the input value in parenthesis. Let subcommands use spaces.

2. 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.

3. Functions can accept expressions while let subcommands do not. For example, the following is legal:
   LET Y2 = ABS(Y1-INT(Y1))

   For let subcommands, you typically have to do something like the following:

   LET YTEMP = Y**2 + 8
   LET A = SUM YTEMP
   

None

None

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.

Allan MacLead (1996), "ACM Transactions of Mathematical Software," Vol. 22, No. 3, pp. 288-301.

Special Functions

1999/6

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