relation to Bessel functions

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2: 10.16 Relations to Other Functions
Elementary Functions
${H^{(2)}_{\frac{1}{2}}}\left(z\right)=i{H^{(2)}_{-\frac{1}{2}}}\left(z\right)=% i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{-iz}.$
3: 18.34 Bessel Polynomials
§18.34(i) Definitions and Recurrence Relation
18.34.1 $y_{n}\left(x;a\right)={{}_{2}F_{0}}\left({-n,n+a-1\atop-};-\frac{x}{2}\right)=% {\left(n+a-1\right)_{n}}\left(\frac{x}{2}\right)^{n}{{}_{1}F_{1}}\left({-n% \atop-2n-a+2};\frac{2}{x}\right)=n!\left(-\tfrac{1}{2}x\right)^{n}L^{(1-a-2n)}% _{n}\left(2x^{-1}\right)=\left(\tfrac{1}{2}x\right)^{1-\frac{1}{2}a}{\mathrm{e% }}^{1/x}W_{1-\frac{1}{2}a,\frac{1}{2}(a-1)+n}\left(2x^{-1}\right).$
where $\mathsf{k}_{n}$ is a modified spherical Bessel function (10.49.9), and …
18.34.8 $\lim_{\alpha\to\infty}\frac{P^{(\alpha,a-\alpha-2)}_{n}\left(1+\alpha x\right)% }{P^{(\alpha,a-\alpha-2)}_{n}\left(1\right)}=y_{n}\left(x;a\right).$
7: 9.13 Generalized Airy Functions
Swanson and Headley (1967) define independent solutions $A_{n}\left(z\right)$ and $B_{n}\left(z\right)$ of (9.13.1) by …
$-A_{n}'\left(0\right)=p^{1/2}B_{n}'\left(0\right)=\frac{p^{p}}{\Gamma\left(p% \right)}.$
10: 9.8 Modulus and Phase
(These definitions of $\theta\left(x\right)$ and $\phi\left(x\right)$ differ from Abramowitz and Stegun (1964, Chapter 10), and agree more closely with those used in Miller (1946) and Olver (1997b, Chapter 11).) …