Dataplot Vol 2 Vol 1

# EN

Name:
EN (LET)
Type:
Library Function
Purpose:
Compute the Euler number or the Euler polynomial.
Description:
The Euler numbers can be defined by the recurrence relation:

where n defines the order of the Euler number and the factorial function, and E(0) = 1. Note that Euler numbers are only defined for 0 and positive even integers.

The Euler polynomials can be defined in terms of the Euler numbers:

where E(k) is the Euler number of order k.

Dataplot computes this function using the EULERB and EULERP routines from "Computation of Special Functions" (see the Reference section below).

Syntax 1:
LET <y> = EN(<x>,<n>)             <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, variable or parameter;
<n> is a non-negagive integer number, variable or parameter;
<y> is a variable or a parameter (depending on what <x> and <n> are) where the computed Euler polynomial values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the Euler polynomial of order .

Syntax 2:
LET <y> = EN(<n>)             <SUBSET/EXCEPT/FOR qualification>
where <n> is a non-negagive integer number, variable or parameter;
<y> is a variable or a parameter (depending on what <n> is) where the computed Euler numbers are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the Euler number of order .

Examples:
LET A = EN(12)
LET A = EN(B)
LET A = EN(2.5,4)
LET Y = EN(X,N)
Default:
None
Synonyms:
None
Related Commands:
 BN = Compute Bernoulli number or polynomial. EULER NUMBERS = Generate a sequence of Euler numbers.
Reference:
"Computation of Special Functions", Shanjie Zhang and Jianming Jin, John Wiley and Sons, 1996, chapter 1.
Applications:
Probability
Implementation Date:
1997/12
Program:
TITLE AUTOMATIC
PLOT EN(X,2) FOR X = 0 0.01 5

Date created: 6/5/2001
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.