In "Bessel function of the first kind with complex argument" paper, authors have expanded a Bessel function $$ J_0(z) $$ with complex argument $$ z=x+i y $$ for $$ |x|\ll 1 $$ and $$ |y|\ll 1. $$ But I want to expand it when $$ |y|\gg|x| $$ or $$|y|\ll|x|$$. Now I am confused that the result of the mentioned article is right for $$ |y|\gg|x| or |y|\ll|x|$$ or not? Please help me!!!!!!!!
2026-03-28 18:12:52.1774721572
Bessel function expansion with complex argument
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