A class of identities relating Whittaker and Bessel functions (Q1876725)

The author uses the Whittaker differential equation to show certain identities between\break \(W_{n+\frac{1}{2},ik}(2x)\), the Whittaker function and modified Bessel functions. The weakly singular differential equation \[ y''+\frac{1-2a}{x}y'+ \biggl[(bcx^{c-1})^{2}+\frac{a^{2}-p^{2}c^{2}}{x^{2}} \biggr]y=0 \] has the solution [\textit{M. Boas}, Mathematical methods in the physical sciences (1966; Zbl 0158.04603), p. 565] \[ y=x^{a}Z_{p}(bx^{c}), \] where \(Z\) stands for \(J\) or \(N\) or any linear combination of them, and \(a,b,c,p\) are constants. The paper [\textit{A. Erdélyi} Monatsh. Math. Phys. 46, 1--9 (1937; JFM 63.0326.01 and Zbl 0017.06502)] could have been included in the bibliography. Reviewer's remark: The purported differential equation for \(W_{n+\frac{1}{2},ik}(2x)\) is not the one given in [\textit{E. T. Whittaker} and \textit{G. N. Watson}, A course of Modern Analysis (1940)]. Also the imaginary index \(ik\) is not the usual one given in the literature.