How to get the asymptotic formula of generalized Bessel function? $$J_{\nu}^{(\mu)}(z)=\frac{2}{\sqrt{\pi}\Gamma(\nu+1-1/\mu)}\Big(\frac{z}{2}\Big)^{\mu \nu/2} \int_{0}^{1} (1-\tau^\mu)^{\nu-1/\mu}\cos z\tau\, \mathrm{d}\tau \quad \Re(\nu)>1/\mu-1,\ \mu\geqslant 1.$$ I can find the Bessel function in books, but I do not know the generalized Bessel function. Can you help me?
2026-03-30 10:38:44.1774867124
How to get the asymptotic formula of generalized Bessel function?
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