DLMF:9.13.E10

MaRDI QIDQ3670

• Label: DLMF:9.13.E10

Digital Library of Mathematical Functions ID 9.13.E10

${\displaystyle{\displaystyle A_{n}\left(-z\right)=\begin{cases}2\sqrt{p/\pi}\cos\left(\tfrac{1}{2}p\pi\right)z^{-n/4}\left(\cos\left(\zeta-\tfrac{1}{4}\pi\right)+e^{|\Im\zeta|}O\left(\zeta^{-1}\right)\right),&\text{$|\operatorname{ph}z|\leq 2p\pi-\delta$, $n$ odd},\\ \sqrt{p/\pi}z^{-n/4}e^{\zeta}\left(1+O\left(\zeta^{-1}\right)\right),&\text{$|\operatorname{ph}z|\leq p\pi-\delta$, $n$ even},\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle A_{\NVar{n}}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\Im}}$: imaginary part
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
• ${\displaystyle{\displaystyle n}}$: parameter (locally)
• ${\displaystyle{\displaystyle p}}$: variable
• ${\displaystyle{\displaystyle\zeta}}$: variable
 

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