110 lines
3.2 KiB
MQL5
110 lines
3.2 KiB
MQL5
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//+------------------------------------------------------------------+
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//| zeta.mqh |
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//| Copyright 2025, MetaQuotes Ltd. |
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//| https://www.mql5.com |
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//+------------------------------------------------------------------+
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#property copyright "Copyright 2025, MetaQuotes Ltd."
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#property link "https://www.mql5.com"
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#include "error.mqh"
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#include "const.mqh"
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namespace special {
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namespace cephes {
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namespace detail {
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/* Expansion coefficients
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* for Euler-Maclaurin summation formula
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* (2k)! / B2k
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* where B2k are Bernoulli numbers
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*/
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double zeta_A[] = {
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12.0,
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-720.0,
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30240.0,
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-1209600.0,
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47900160.0,
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-1.8924375803183791606e9, /*1.307674368e12/691 */
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7.47242496e10,
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-2.950130727918164224e12, /*1.067062284288e16/3617 */
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1.1646782814350067249e14, /*5.109094217170944e18/43867 */
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-4.5979787224074726105e15, /*8.028576626982912e20/174611 */
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1.8152105401943546773e17, /*1.5511210043330985984e23/854513 */
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-7.1661652561756670113e18 /*1.6938241367317436694528e27/236364091 */
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};
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/* 30 Nov 86 -- error in third coefficient fixed */
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} // namespace detail
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double inline zeta(double x, double q) {
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int i;
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double a, b, k, s, t, w;
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if (x == 1.0)
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return (infinity());
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if (x < 1.0) {
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set_error("zeta", SF_ERROR_DOMAIN, NULL);
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return (quiet_NaN());
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}
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if (q <= 0.0) {
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if (q == floor(q)) {
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set_error("zeta", SF_ERROR_SINGULAR, NULL);
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return (infinity());
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}
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if (x != floor(x))
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{
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set_error("zeta", SF_ERROR_DOMAIN, NULL);
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return (quiet_NaN());
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}
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}
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/* Asymptotic expansion
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* https://dlmf.nist.gov/25.11#E43
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*/
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if (q > 1e8) {
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return (1 / (x - 1) + 1 / (2 * q)) * pow(q, 1 - x);
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}
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/* Euler-Maclaurin summation formula */
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/* Permit negative q but continue sum until n+q > +9 .
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* This case should be handled by a reflection formula.
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* If q<0 and x is an integer, there is a relation to
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* the polyGamma function.
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*/
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s = pow(q, -x);
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a = q;
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i = 0;
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b = 0.0;
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while ((i < 9) || (a <= 9.0)) {
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i += 1;
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a += 1.0;
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b = pow(a, -x);
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s += b;
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if (abs(b / s) < detail::MACHEP)
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return (s);
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}
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w = a;
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s += b * w / (x - 1.0);
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s -= 0.5 * b;
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a = 1.0;
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k = 0.0;
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for (i = 0; i < 12; i++) {
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a *= x + k;
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b /= w;
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t = a * b / detail::zeta_A[i];
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s = s + t;
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t = abs(t / s);
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if (t < detail::MACHEP)
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return (s);
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k += 1.0;
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a *= x + k;
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b /= w;
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k += 1.0;
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}
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return (s);
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}
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} // namespace cephes
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} // namespace special
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