Dataplot Vol 2 Vol 1

# I0INT

Name:
I0INT (LET)
Type:
Library Function
Purpose:
This program computes the integral of the modified Bessel function I0(x).
Description:
The I0INT function is defined as:

with I0 denoting the modified Bessel function of the first kind of order 0.

Dataplot computes this function using ACM Algorithm 757 (see Reference: below). The function is computed using Chebyshev expansions, the coefficients of which are given to 20 decimal places.

Syntax:
LET <y> = I0INT(<x>)             <SUBSET/EXCEPT/FOR qualification>br> where <x> is a non-negative number, variable or parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed I0INT function values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = I0INT(2.3)
PLOT I0INT(X) FOR X = 0 .01 10
LET X2 = I0INT(X1) FOR X1 = 0.1 0.1 3.0
Default:
None
Synonyms:
None
Related Commands:
 BESSI0 = Compute the modified Bessel function of the first kind and order 0. BESSI1 = Compute the modified Bessel function of the first kind and order 1. BESSIN = Compute the modified Bessel function of the first kind and order N. BESSJN = Compute the Bessel function of the first kind and order N. BESSKN = Compute the modified Bessel function of the third kind and order N. BESSYN = Compute the Bessel function of the second kind and J0INT = Compute the integral of the Bessel function of the first kind and order 0. K0INT = Compute the integral of the modified Bessel function of the third kind and order 0. Y0INT = Compute the integral of the Bessel function of the second kind and order 0. I0ML0 = Compute the difference of the modified Bessel function of the first kind of order 0 and the modified Struve function of order 0. I1ML1 = Compute the difference of the modified Bessel function of the first kind of order 1 and the modified Struve function of order 1.
Reference:
"ACM Transactions of Mathematical Software", Allan MacLead, Vol. 22, No. 3, September, 1996, pp. 288-301.
Applications:
Special Functions
Implementation Date:
2005/11
Program:
```
TITLE I0INT FUNCTION
PLOT I0INT(X) FOR X = 0 0.01 10
```

Date created: 11/7/2005
Last updated: 11/7/2005