Let us consider $J_0()$ as the zero-order Bessel function of the first kind, and $\alpha$ and $\beta$ as constants. Then, is it possible to write $J_0(\alpha \sqrt{i^3\beta})$ in terms of $J_0(\alpha\sqrt{i\beta})$? In other words, what is the relation between $J_0(\alpha \sqrt{i^3\beta})$ and $J_0(\alpha \sqrt{i\beta})$? Please help me.
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1The first one is basically an $I_0$ modified Bessel function. – Gary Apr 21 '23 at 11:17