Class bessel_K_exp_integ_direct (o2scl)¶
-
template<class
fp_t
= double, classfunc_t
= funct_ld, size_tmax_refine
= 15, classinternal_fp_t
= long double>
classo2scl
::
bessel_K_exp_integ_direct
¶ Compute exponentially scaled modified bessel function of the second kind by direct integration.
This class computes \( K_n(z) e^z\) for \( n=1,2,3 \) by directly integrating. It integrates the representation
\[ K_n(z) e^{z} = \frac{\sqrt{\pi} z^{n}}{2^{n} \Gamma(n+1/2)} \int_1^{\infty} e^{z(1-t)} \left(t^2-1\right)^{n-1/2}~dt \](see http://functions.wolfram.com/Bessel-TypeFunctions/BesselK/07/01/01/) by applying an integrator (of type o2scl::bessel_K_exp_integ_tl) with a larger floating point type and then casting the result back tofp
t. This should work with boost multiprecision types but is only currently tested withinternal_fp_t=long double
.With the default types, this class should give almost identical results to o2scl::bessel_K_exp_integ_gsl .
Public Functions
-
bessel_K_exp_integ_direct
()¶
Protected Attributes
-
bessel_K_exp_integ_tl<o2scl::inte_exp_sinh_boost<func_t, max_refine, internal_fp_t>, internal_fp_t>
it
¶ The integrator.
-