Bessel–Clifford function

Summary

The Bessel–Clifford function $\mathcal{C}_n$ is an entire function of one variable. It is the Bessel function of the first kind without its power factor and its square root. It satisfies $J_n(x) = \left( \frac{x}{2} \right)^n \mathcal{C}_n\left( -\frac{x^2}{4} \right)$. Its power series has the simple coefficients $\frac{1}{k!\, \Gamma(n + k + 1)}$, which makes it convenient in computation and in algebraic arguments.