Dataplot Vol 2 Vol 1

# BERNOULLI NUMBERS

Name:
BERNOULLI NUMBERS (LET)
Type:
Let Subcommand
Purpose:
Generate a sequence of Bernoulli numbers.
Description:
For a description of Bernoulli numbers and polynomials, enter the command:

HELP BN

BN is a library function for computing Bernoulli numbers and polynomials. The BERNOULLI NUMBERS command can be used to generate a sequence of Bernoulli numbers.

Syntax:
LET <y> = BERNOULLI NUMBERS FOR I = <start> <inc> <stop>
where <start> is the starting row for the Bernoulli numbers;
<inc> is the increment for the Bernoulli numbers;
<stop> is the stopping row for the Bernoulli numbers;
<y> is a variable where the Bernoulli numbers are saved.

Typically and are 1 and is set to the number of Bernoulli numbers to generate. If and are not 1, then will still contain elements, but the empty rows will be set to 0.

Examples:
LET Y = BERNOULLI NUMBERS FOR I = 1 1 50
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:
LET Y = BERNOULLI NUMBERS FOR I = 1 1 50
PRINT Y

The following output is generated.

```
VARIABLES--Y

0.1000000E+01
-0.5000000E+00
0.1666667E+00
0.0000000E+00
-0.3333334E-01
0.0000000E+00
0.2380952E-01
0.0000000E+00
-0.3333334E-01
0.0000000E+00
0.7575758E-01
0.0000000E+00
-0.2531136E+00
0.0000000E+00
0.1166667E+01
0.0000000E+00
-0.7092157E+01
0.0000000E+00
0.5497118E+02
0.0000000E+00
-0.5291243E+03
0.0000000E+00
0.6192123E+04
0.0000000E+00
-0.8658025E+05
0.0000000E+00
0.1425517E+07
0.0000000E+00
-0.2729823E+08
0.0000000E+00
0.6015809E+09
0.0000000E+00
-0.1511632E+11
0.0000000E+00
0.4296146E+12
0.0000000E+00
-0.1371165E+14
0.0000000E+00
0.4883323E+15
0.0000000E+00
-0.1929658E+17
0.0000000E+00
0.8416931E+18
0.0000000E+00
-0.4033807E+20
0.0000000E+00
0.2115075E+22
0.0000000E+00
-0.1208663E+24
0.0000000E+00

```

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