These lines (561-567) of src/nmath/bessel_j.c seem relevant. :-)
L250:
/* ---------------------------------------------------
Normalize. Divide all b[N] by sum.
---------------------------------------------------*/
/* if (nu + 1. != 1.) poor test */
if(fabs(nu) > 1e-15)
sum *= (Rf_gamma_cody(nu) * pow(.5* *x, -nu));
Mikael
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