Question about calculate the Bessel function with IMSL

[Chang_Pai_L_]

Ver. Intel Composer XE2013 with Visual Studio 2010 Ultimate

I want to solve the problem about BesselI0/BesselI1 with using the IMSL. Problem is one extreme value divided by another one extreme value and the result should be an uncomplicated value.   

Unfortunately, I can not calculate when input data over 700, the output data over 300 order, modified Bessel function of the zero and first kind data will present 'infinite' .

My PROBLEM like (double precision)

'"M(I)=DBSI0(L1(I))/DBSI1(L1(I))""    L1(I)  are real data, The  "problem" happened in L1(I)>700, the M(I) output "NaN" result.

How could I calculate this vector?

Thanks for any help!!

[mecej4]

See if you can use Hankel's asymptotic expansions for I₀ and I₁ ( https://en.wikipedia.org/wiki/Bessel_function#Asymptotic_forms ). Using those expansions, you can write the ratio I₀(z)/I₁(z) as the ratio of two power series in 1/z. The leading factor, e^z/sqrt(z), which causes I₀ and I₁ to become very large, occurs in both the numerator and the denominator, so you can cancel it out.

For values of z with modulus as large as 700, you should be able to obtain accurate results with a small number of terms in the series.

[Chang_Pai_L_]

Thanks for useful reply!