44 lines
1.0 KiB
C
44 lines
1.0 KiB
C
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#include <stdio.h>
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#include <math.h>
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#include <stdlib.h>
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/* Compute the Euler_Mascheroni constant through the formula:
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*
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* γ = lim_{M → +inf} sum_{k = 1}^{M} bin{M, k} (-1)^k / k * ln(Γ(k+1))
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*
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* Best result is obtained for M = 41.
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* Values from 1 to 100 were checked.
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*
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*/
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double exact = 0.577215664901532860;
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int main() {
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double best = 0, num = 0;
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double sum = 0, prev;
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for (double M = 1; M < 60; M++) {
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prev = sum;
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sum = 0;
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for (double k = 1; k <= M; k++) {
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sum += (tgamma(M + 1))/(tgamma(k + 1)*tgamma(M - k + 1)) * pow(-1, k)/k
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* log(tgamma (k + 1));
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}
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printf("M: \t%d\t", (int)M);
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printf("diff:\t%.15f\n", fabs(sum - exact));
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if ((fabs(sum - exact) < fabs(prev - exact)) &&
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(fabs(sum - exact) < fabs(best - exact))){
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best = sum;
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num = M;
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}
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}
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printf("M: %d\n", (int)num);
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printf("approx:\t%.15f\n", best);
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printf("true:\t%.15f\n", exact);
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printf("diff:\t%.15f\n", fabs(best - exact));
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printf("\t 123456789_12345\n");
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return EXIT_SUCCESS;
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}
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