Relation between $J_0(\alpha \sqrt{i^3\beta})$ and $J_0(\alpha \sqrt{i\beta})$

24 Views Asked by At

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.