reflection properties in ν

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11: 4.37 Inverse Hyperbolic Functions

… ►Elsewhere on the integration paths in (4.37.1) and (4.37.2) the branches are determined by continuity. In (4.37.3) the integration path may not intersect $\pm 1$. … ►These functions are analytic in the cut plane depicted in Figure 4.37.1(iv), (v), (vi), respectively. … ►

§4.37(iii) Reflection Formulas

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§4.37(v) Fundamental Property

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12: 10.47 Definitions and Basic Properties

§10.47 Definitions and Basic Properties

… ►(This is in contrast to other treatments of spherical Bessel functions, including Abramowitz and Stegun (1964, Chapter 10), in which $n$ can be any integer. … ►Many properties of ${𝗃}_n\left(z\right)$, ${𝗒}_n\left(z\right)$, ${𝗁}_n^{(1)}\left(z\right)$, ${𝗁}_n^{(2)}\left(z\right)$, ${𝗂}_n^{(1)}\left(z\right)$, ${𝗂}_n^{(2)}\left(z\right)$, and ${𝗄}_n\left(z\right)$ follow straightforwardly from the above definitions and results given in preceding sections of this chapter. … … ►

§10.47(v) Reflection Formulas

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13: 4.23 Inverse Trigonometric Functions

… ►These functions are analytic in the cut plane depicted in Figures 4.23.1(iii) and 4.23.1(iv). … ►Graphs of the principal values for real arguments are given in §4.15. … ►

§4.23(iii) Reflection Formulas

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§4.23(v) Fundamental Property

►With $k\in \mathbb{Z}$, the general solutions of the equations …