1/*
2 * bernpoly - Bernoulli polynomials B_n(z) for arbitrary n,z..
3 *
4 * Copyright (C) 2013,2021 Christoph Zurnieden
5 *
6 * Calc is open software; you can redistribute it and/or modify it under
7 * the terms of the version 2.1 of the GNU Lesser General Public License
8 * as published by the Free Software Foundation.
9 *
10 * Calc is distributed in the hope that it will be useful, but WITHOUT
11 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
12 * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
13 * Public License for more details.
14 *
15 * A copy of version 2.1 of the GNU Lesser General Public License is
16 * distributed with calc under the filename COPYING-LGPL.  You should have
17 * received a copy with calc; if not, write to Free Software Foundation, Inc.
18 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
19 *
20 * Under source code control:	2013/08/11 01:31:28
21 * File existed as early as:	2013
22 */
23
24
25static resource_debug_level;
26resource_debug_level = config("resource_debug", 0);
27
28
29read -once zeta2
30
31
32/* Idea by Don Zagier */
33define bernpoly(n,z){
34  local h s c k;
35  if(isint(n) && n>=0){
36    h=0;s=0;c=-1;
37    for(k=1;k<=n+1;k++){
38      c*=1-(n+2)/k;
39      s+=z^n;
40      z++;
41      h+=c*s/k;
42    }
43    return h;
44  }
45  else return -n*hurwitzzeta(1-n,z);
46}
47
48
49/*
50 * restore internal function from resource debugging
51 */
52config("resource_debug", resource_debug_level),;
53if (config("resource_debug") & 3) {
54    print "bernpoly(n,z)";
55}
56