I have a product Exp[-I*Pi*x]*BesselK[-1, 2.43*Ix]
. Now, Exp[-I*Pi*x]
grows larger and larger as $x$ increases for imaginary large values, while BesselK[-1, 2.43*Ix]
decreases. At a particular large imaginary value of $x$, while the product is finite, Exp[-I*Pi*x]
is very large while BesselK[-1, 2.43*Ix]
is around $10^{-300}$ and Mathematica sets the latter to be equal to zero, which makes the product become equal to zero.
Is there a way to tell Mathematica not to do this?
The exact input is:
Exp[-I*Pi*x]*BesselK[-1, 2.43*I*x] /. x -> I*290 // N
This returns -1.97747*10^88 - 2.456351670414645*10^700
I
If I write: Exp[-I*Pi*x]*BesselK[-1, 2.43*I*x] /. x -> I*291 // N
then it returns 0. - 6.445487767605421*10^702 I
So, there is a jump in the transition of x=290
to x=291
ix
or ratherI x
? $\endgroup$ix
? Somthing likeI x
? $\endgroup$