# reflection properties

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## 1—10 of 13 matching pages

##### 1: 28.12 Definitions and Basic Properties
28.12.2 $\lambda_{\nu}\left(-q\right)=\lambda_{\nu}\left(q\right)=\lambda_{-\nu}\left(q% \right).$
28.12.15 $\operatorname{se}_{\nu}\left(z,q\right)=-\operatorname{se}_{\nu}\left(-z,q% \right)=-\operatorname{se}_{-\nu}\left(z,q\right).$
##### 2: 28.5 Second Solutions $\operatorname{fe}_{n}$, $\operatorname{ge}_{n}$
$S_{2m+2}(-q)=S_{2m+2}(q).$
##### 3: 28.2 Definitions and Basic Properties
###### Change of Sign of $q$
28.2.37 $\operatorname{se}_{2n+2}\left(z,-q\right)=(-1)^{n}\operatorname{se}_{2n+2}% \left(\tfrac{1}{2}\pi-z,q\right).$
##### 5: 28.31 Equations of Whittaker–Hill and Ince
$\mathit{hs}_{2n+2}^{2m+2}(z,-\xi)=(-1)^{m}\mathit{hs}_{2n+2}^{2m+2}(\tfrac{1}{% 2}\pi-z,\xi).$
##### 6: 31.8 Solutions via Quadratures
The curve $\Gamma$ reflects the finite-gap property of Equation (31.2.1) when the exponent parameters satisfy (31.8.1) for $m_{j}\in\mathbb{Z}$. …
##### 7: 10.68 Modulus and Phase Functions
###### §10.68(ii) Basic Properties
$\phi_{-\nu}\left(x\right)=\phi_{\nu}\left(x\right)+\nu\pi.$
###### §10.68(iv) Further Properties
Additional properties of the modulus and phase functions are given in Young and Kirk (1964, pp. xi–xv). …
##### 8: 10.61 Definitions and Basic Properties
###### §10.61 Definitions and Basic Properties
Most properties of $\operatorname{ber}_{\nu}x$, $\operatorname{bei}_{\nu}x$, $\operatorname{ker}_{\nu}x$, and $\operatorname{kei}_{\nu}x$ follow straightforwardly from the above definitions and results given in preceding sections of this chapter. …
##### 9: 11.9 Lommel Functions
###### Reflection Formulas
For descriptive properties of $s_{{\mu},{\nu}}\left(x\right)$ see Steinig (1972). …
##### 10: 4.37 Inverse Hyperbolic Functions
4.37.6 $\operatorname{Arccoth}z=\operatorname{Arctanh}\left(1/z\right).$