I need to know an equivalent expression for lommel function with these parameters as follow : S(-ν-1,ν) (z) for ν > 0 and all z and v can be integer or not.
I read the book (p.348-349) "A Treatise on the Theory of Bessel Functions" following link : https://archive.org/details/ATreatiseOnTheTheoryOfBesselFunctions/page/n357/mode/2up?q=%C2%A710.73
But I noticed that if I want use the relation ['10.73 (1)' in above book] then p = v so the term of 1/(v-p)m+1 ("pochhamer function") in summation goes to infinity. So what can I do? Also I'm interested in this case that what would be the limit on lommel when v >> 1 I woud appreciat it if someone can help. thanks.