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Riemann Zeta Function
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#include <stdio.h> | |
#include <math.h> | |
double lim(double (*f)(double), double p) | |
{ | |
double a(int n) | |
{ | |
if (isinf(p)) { | |
return pow(2, n); | |
} | |
else if (p == 0) { | |
return 1 / pow(2, n); | |
} | |
return n; | |
} | |
double L; | |
double x; | |
int n; | |
for (n = 1;; n++) { | |
x = a(n); | |
L = f(a(n + 1)); | |
if (fabs(f(x) - L) == 0) { | |
return L; | |
} | |
} | |
} | |
double sum(double (*f)(double), int m, double n) | |
{ | |
if (isfinite(n)) { | |
if (m > n) { | |
return 0; | |
} | |
return f(n) + sum(f, m, n - 1); | |
} | |
else { | |
double g(double n) | |
{ | |
return sum(f, m, n); | |
} | |
return lim(g, INFINITY); | |
} | |
} | |
int factorial(int n) | |
{ | |
if (n == 0) { | |
return 1; | |
} | |
return n * factorial(n - 1); | |
} | |
double exp(double x) | |
{ | |
double f(double n) | |
{ | |
return pow(x, n) / factorial(n); | |
} | |
return sum(f, 0, INFINITY); | |
} | |
double D(double (*f)(double), double a) | |
{ | |
double g(double h) | |
{ | |
return (f(a + h) - f(a)) / h; | |
} | |
return lim(g, 0); | |
} | |
double zeta(double s) | |
{ | |
double f(double n) | |
{ | |
return pow(n, -s); | |
} | |
return sum(f, 1, INFINITY); | |
} | |
int main(void) | |
{ | |
printf("%g\n", zeta(0)); | |
return 0; | |
} |
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function lim(f, p) { | |
var e = Number.MIN_VALUE; | |
var a; | |
switch (p) { | |
case 0: | |
a = function(n) { | |
return 1 / Math.pow(2, n); | |
}; | |
case Infinity: | |
a = function(n) { | |
return Math.pow(2, n); | |
}; | |
} | |
for (var n = 1;; n++) { | |
var L = f(a(n + 1)); | |
var x = a(n); | |
if (Math.abs(f(x) - L) < e) { | |
return L; | |
} | |
} | |
} | |
function D(f) { | |
return function(a) { | |
return lim(function(h) { return (f(a + h) - f(a)) / h }, 0); | |
}; | |
} | |
function sum(f, m, n) { | |
if (isFinite(n)) { | |
if (m > n) { | |
return 0; | |
} | |
return f(n) + sum(f, m, n - 1); | |
} | |
else { | |
return lim(function(n) { return sum(f, m, n) }, Infinity); | |
} | |
} | |
function product(f, m, n) { | |
if (isFinite(n)) { | |
if (m > n) { | |
return 1; | |
} | |
return f(n) * product(f, m, n - 1); | |
} | |
else { | |
return lim(function(n) { return product(f, m, n) }, Infinity); | |
} | |
} | |
function factorial(n) { | |
if (n == 0) { | |
return 1; | |
} | |
return n * factorial(n - 1); | |
} | |
PI = 1 / (2 * Math.sqrt(2) / 9801 * sum(function(k) { | |
return factorial(4 * k) * (1103 + 26390 * k) / | |
(Math.pow(factorial(k), 4) * Math.pow(396, 4 * k)); | |
}, 0, Infinity)); | |
function exp(x) { | |
return sum(function(n) { return Math.pow(x, n) / factorial(n) }, 0, Infinity); | |
} | |
function B(n) { | |
return (n == 0 ? 1 : 0) - sum(function(k) { | |
return C(n, k) * B(k) / (n - k + 1); | |
}, 0, n - 1); | |
} | |
function C(n, k) { | |
if (k == 0) { | |
return 1; | |
} | |
if (n == 0) { | |
return 0; | |
} | |
return C(n - 1, k - 1) + C(n - 1, k); | |
} | |
function zeta(s) { | |
return sum(function(n) { return Math.pow(n, -s) }, 1, Infinity); | |
} |
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