 Dataplot Vol 2 Vol 1

# BN

Name:
BN (LET)
Type:
Library Function
Purpose:
Compute the Bernoulli number or the Bernoulli polynomial.
Description:
The Bernoulli numbers can be defined by the recurrence relation: where N defines the order of the Bernouilli numbers and "!" is the factorial function, and B(0) = 1.

The Bernoulli polynomials can be defined in terms of the Bernoulli numbers: where BINOM is the binomial coefficient function (n!/(k!(n-k)!), and B(k) is the Bernoulli number of order k.

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

Syntax 1:
LET <y> = BN(<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 Bernoulli polynomial values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the Bernoulli polynomial of order .

Syntax 2:
LET <y> = BN(<n>)             <SUBSET/EXCEPT/FOR qualification>
where <n> is a non-negagive integer number, variable or parameter; and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the Bernoulli number of order .

Examples:
LET A = BN(12)
LET A = BN(B)
LET A = BN(2.5,4)
LET Y = BN(X,N)
Default:
None
Synonyms:
None
Related Commands:
 BINCDF = Compute the binomial cumulative distribution function. BINPDF = Compute the binomial probability mass function. BINPPF = Compute the binomial percent point function. BINOMIAL = Compute the binomial coefficients. EN = Compute Euler number or polynomial.
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 BERNOULLI POLYNOMIAL OF ORDER 2
LET X = SEQUENCE 0 0.01 5
LET Y = BN(X,2)
RETAIN X Y SUBSET Y > 0
YLIMTIS 0 20
YTIC OFFSET 0 1
PLOT Y X

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