At Wed, 25 Aug 2010 23:41:14 -0400,
Alexey A. Illarionov wrote:
> It seems that I find a bug in gsl_sf_coulomb_wave_FG_e. For large values
> of lambda and small values of x, with eta = 0 it produces nan values
> without raising of the flag.
>
> Here the sample cases (see attachment with example)
> gsl_sf_coulomb_wave_FG_e(0.,1.2693881947287221e-07, 37, 1, ...)
> gsl_sf_coulomb_wave_FG_e(0.,5.911135077240691e-07, 39, 1, ...)
> gsl_sf_coulomb_wave_FG_e(0.,6.118185507743884e-07, 40, 1, ...)
> and lots of others.
Thanks for the bug report. I'm adding a test case for this. Can you
confirm if the following values are correct (I'm not working with
these functions often):
lam_F = 37.0;
eta = 0.0;
x = 1.2693881947287221e-07;
k_G = 1;
gsl_sf_coulomb_wave_FG_e(eta, x, lam_F, k_G, &F, &Fp, &G, &Gp, &Fe, &Ge);
s = 0;
message_buff[0] = 0;
s += test_sf_check_result(message_buff, F,
-2.020327525317343313380459069e299, TEST_TOL3);
s += test_sf_check_result(message_buff, Fp,
5.729672862364037942289798904e307, TEST_TOL3);
s += test_sf_check_result(message_buff, G,
4.397355593129492554472984282e299, TEST_TOL3);
s += test_sf_check_result(message_buff, Gp, -
1.247095270068213211088454516e308, TEST_TOL3);
I've computed them using Pari as
c(L,n) = { 2^L * exp(-Pi*n/2) * abs(gamma(L+1+I*n)) / gamma(2*L+2)}
cofac(L,n,r) = { I * exp(-I*r)*r^(-L)/(gamma(2*L+2)*c(L,n)) }
FplusIG(L,n,r) = { cofac(L,n,r) *
intnum(t=0,[[1],1],exp(-t)*t^(L-I*n)*(t+2*I*r)^(L+I*n)) }
FplusIG(37,0,1.2693881947287221e-07+x) # for F and F' (real part)
FplusIG(36,0,1.2693881947287221e-07+x) # for G and G' (imaginary part)
--
Brian Gough
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