Dataplot Vol 2 Vol 1

# KER

Name:
KER (LET)
Type:
Library Function
Purpose:
Compute the ker Kelvin function or the derivative of the ker Kelvin function.
Description:
The ker Kelvin functions can define in terms of the Bessel function of the third kind:

where Kv is the Bessel function of the third kind.

The functions described here compute these functions for the case when there is a real, non-negative input argument and order zero (i.e., v = 0).

Dataplot computes these function using the KLVNA routines from "Computation of Special Functions" (see the References section below).

Syntax 1:
LET <yr> = KER(<x>)             <SUBSET/EXCEPT/FOR qualification>
where <x> is a non-negative number, variable or parameter;
<yr> is a variable or a parameter (depending on what <x> is) where the computed Kelvin value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the real component of the ker Kelvin function.

Syntax 2:
LET <yc> = KERI(<x>)             <SUBSET/EXCEPT/FOR qualification>
where <x> is a non-negative number, variable or parameter;
<yc> is a variable or a parameter (depending on what <x> is) where the computed Kelvin value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the complex component of the ker Kelvin function.

Syntax 3:
LET <yr> = KER1(<x>)             <SUBSET/EXCEPT/FOR qualification>
where <x> is a non-negative number, variable or parameter;
<yr> is a variable or a parameter (depending on what <x> is) where the computed Kelvin value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the real component of the derivative of the ker Kelvin function.

Syntax 4:
LET <yc> = KERI1(<x>) <SUBSET/EXCEPT/FOR qualification>
where <x> is a non-negative number, variable or parameter;
<yc> is a variable or a parameter (depending on what <x> is) where the computed Kelvin value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the complex component of the derivative of the ker Kelvin function.

Examples:
LET A = KER(2)
LET A = KERI(2)
LET A = KER1(2)
LET A = KERI1(2)

LET YR = KER(X)
LET YC = KERI(X)

Default:
None
Synonyms:
None
Related Commands:
 BER = Compute the BER Kelvin functions. CBESSJ = Compute the Bessel function of the first kind with complex argument. CBESSY = Compute the Bessel function of the second kind with complex argument. CBESSI = Compute the modified Bessel function with complex argument. CBESSK = Compute the modified Bessel function of the third kind with complex argument. BESSKN = Compute the Bessel function of the third kind with real argument. BESSIN = Compute the modified Bessel function with real argument. BESSJN = Compute the Bessel function of the first kind with real argument.
Reference:
"Computation of Special Functions", Shanjie Zhang and Jianming Jin, John Wiley and Sons, 1996, chapter 9.

"Handbook of Mathematical Functions, Applied Mathematics Series, Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 1964 (pages 379-385).

Applications:
Special Functions
Implementation Date:
1997/12
Program:
LINE SOLID DASH
TITLE KER KELVIN FUNCTION
PLOT KER(X) FOR X = 0.1 0.1 10 AND
PLOT KERI(X) FOR X = 0.1 0.1 10

Date created: 6/5/2001
Last updated: 4/4/2003