How to resolve the algorithm Bernoulli numbers step by step in the GAP programming language

Published on 12 May 2024 09:40 PM
#Gap

How to resolve the algorithm Bernoulli numbers step by step in the GAP programming language

Table of Contents

Problem Statement

Bernoulli numbers are used in some series expansions of several functions   (trigonometric, hyperbolic, gamma, etc.),   and are extremely important in number theory and analysis. Note that there are two definitions of Bernoulli numbers;   this task will be using the modern usage   (as per   The National Institute of Standards and Technology convention). The   nth   Bernoulli number is expressed as   Bn.

The Akiyama–Tanigawa algorithm for the "second Bernoulli numbers" as taken from wikipedia is as follows:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Bernoulli numbers step by step in the GAP programming language

Source code in the gap programming language

for a in Filtered(List([0 .. 60], n -> [n, Bernoulli(n)]), x -> x[2] <> 0) do
    Print(a, "\n");
od;

[ 0, 1 ]
[ 1, -1/2 ]
[ 2, 1/6 ]
[ 4, -1/30 ]
[ 6, 1/42 ]
[ 8, -1/30 ]
[ 10, 5/66 ]
[ 12, -691/2730 ]
[ 14, 7/6 ]
[ 16, -3617/510 ]
[ 18, 43867/798 ]
[ 20, -174611/330 ]
[ 22, 854513/138 ]
[ 24, -236364091/2730 ]
[ 26, 8553103/6 ]
[ 28, -23749461029/870 ]
[ 30, 8615841276005/14322 ]
[ 32, -7709321041217/510 ]
[ 34, 2577687858367/6 ]
[ 36, -26315271553053477373/1919190 ]
[ 38, 2929993913841559/6 ]
[ 40, -261082718496449122051/13530 ]
[ 42, 1520097643918070802691/1806 ]
[ 44, -27833269579301024235023/690 ]
[ 46, 596451111593912163277961/282 ]
[ 48, -5609403368997817686249127547/46410 ]
[ 50, 495057205241079648212477525/66 ]
[ 52, -801165718135489957347924991853/1590 ]
[ 54, 29149963634884862421418123812691/798 ]
[ 56, -2479392929313226753685415739663229/870 ]
[ 58, 84483613348880041862046775994036021/354 ]
[ 60, -1215233140483755572040304994079820246041491/56786730 ]

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