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).
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
where <n> is a non-negagive integer number, variable or parameter;
This syntax computes the Bernoulli number of order
LET A = BN(B)
LET A = BN(2.5,4)
LET Y = BN(X,N)
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