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another integral, suggested by Silviu Ioan-Filip

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Fredrik Johansson 2018-01-22 19:02:22 +01:00
parent 17d82b3326
commit 60727fbc8b
1 changed files with 36 additions and 2 deletions
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38
examples/integrals.c
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@ -540,7 +540,7 @@ f_lambertw(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
return 0;
}
/* f(x) = max(sin(x), cos(x)) */
/* f(z) = max(sin(z), cos(z)) */
int
f_max_sin_cos(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
{
@ -571,11 +571,38 @@ f_max_sin_cos(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
return 0;
}
/* f(z) = erf(z/sqrt(0.0002)*0.5 +1.5)*exp(-z), example provided by Silviu-Ioan Filip */
int
f_erf_bent(acb_ptr res, const acb_t z, void * param, slong order, slong prec)
{
acb_t t;
if (order > 1)
flint_abort(); /* Would be needed for Taylor method. */
acb_init(t);
acb_set_ui(t, 1250);
acb_sqrt(t, t, prec);
acb_mul(t, t, z, prec);
acb_set_d(res, 1.5);
acb_add(res, res, t, prec);
acb_hypgeom_erf(res, res, prec);
acb_neg(t, z);
acb_exp(t, t, prec);
acb_mul(res, res, t, prec);
acb_clear(t);
return 0;
}
/* ------------------------------------------------------------------------- */
/* Main test program */
/* ------------------------------------------------------------------------- */
#define NUM_INTEGRALS 25
#define NUM_INTEGRALS 26
const char * descr[NUM_INTEGRALS] =
{
@ -604,6 +631,7 @@ const char * descr[NUM_INTEGRALS] =
"N(1000) = count zeros with 0 < t <= 1000 of zeta(s) using argument principle",
"int_0^{1000} W_0(x) dx",
"int_0^pi max(sin(x), cos(x)) dx",
"int_{-1}^1 erf(x/sqrt(0.0002)*0.5+1.5)*exp(-x) dx",
};
int main(int argc, char *argv[])
@ -997,6 +1025,12 @@ int main(int argc, char *argv[])
acb_calc_integrate(s, f_max_sin_cos, NULL, a, b, goal, tol, options, prec);
break;
case 25:
acb_set_si(a, -1);
acb_set_si(b, 1);
acb_calc_integrate(s, f_erf_bent, NULL, a, b, goal, tol, options, prec);
break;
default:
abort();
}