I think these 2 limits should be 1 not a noun form and the questions are unnecessary. My wish list is for the bessel functions to work this way. Also the ones approaching infinity should be added to my wish list.
(%i1) assume(a>0);
(%o1) [a>0]
.
.
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(%i7) limit(bessel_i(a,x)/(1/gamma(a+1)*(x/2)^a),x,0);
Is bessel_i(a,0)*gamma(a+1) positive, negative, or zero?zero;
Is a-1 positive, negative, or zero?pos;
Is a an integer?no;
(%o7) 2^a*gamma(a+1)*(limit(bessel_i(a,x)/x^a,x,0))
(%i8) limit(bessel_i(a,x)/(1/gamma(a+1)*(x/2)^a),x,0);
Is bessel_i(a,0)*gamma(a+1) positive, negative, or zero?zero;
Is a-1 positive, negative, or zero?neg;
Is a an integer?no;
(%o8) 2^a*gamma(a+1)*(limit(bessel_i(a,x)/x^a,x,0))
Rich