# for large |γ2|

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##### 1: 30.9 Asymptotic Approximations and Expansions
###### §30.9(i) Prolate Spheroidal Wave Functions
The behavior of $\lambda^{m}_{n}\left(\gamma^{2}\right)$ for complex $\gamma^{2}$ and large $|\lambda^{m}_{n}\left(\gamma^{2}\right)|$ is investigated in Hunter and Guerrieri (1982).
##### 2: 30.16 Methods of Computation
If $|\gamma^{2}|$ is large we can use the asymptotic expansions in §30.9. … If $|\gamma^{2}|$ is large, then we can use the asymptotic expansions referred to in §30.9 to approximate $\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)$. …
##### 3: 10.74 Methods of Computation
If $x$ or $|z|$ is large compared with $|\nu|^{2}$, then the asymptotic expansions of §§10.17(i)10.17(iv) are available. … And since there are no error terms they could, in theory, be used for all values of $z$; however, there may be severe cancellation when $|z|$ is not large compared with $n^{2}$. …
##### 4: 15.12 Asymptotic Approximations
If $|\operatorname{ph}z|<\pi$, then as $\lambda\to\infty$ with $|\operatorname{ph}\lambda|\leq\tfrac{1}{2}\pi-\delta$, …
##### 5: 11.6 Asymptotic Expansions
###### §11.6(i) Large$|z|$, Fixed $\nu$
If the series on the right-hand side of (11.6.1) is truncated after $m(\geq 0)$ terms, then the remainder term $R_{m}(z)$ is $O\left(z^{\nu-2m-1}\right)$. If $\nu$ is real, $z$ is positive, and $m+\tfrac{1}{2}-\nu\geq 0$, then $R_{m}(z)$ is of the same sign and numerically less than the first neglected term. …
##### 6: 10.40 Asymptotic Expansions for Large Argument
10.40.2 $K_{\nu}\left(z\right)\sim\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\sum_{% k=0}^{\infty}\frac{a_{k}(\nu)}{z^{k}},$ $|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta$,
##### 7: 2.11 Remainder Terms; Stokes Phenomenon
For large $|z|$, with $|\operatorname{ph}z|\leq\frac{3}{2}\pi-\delta$ ($<\frac{3}{2}\pi$), the Whittaker function of the second kind has the asymptotic expansion (§13.19) …
##### 8: 15.19 Methods of Computation
The Gauss series (15.2.1) converges for $|z|<1$. … Large values of $|a|$ or $|b|$, for example, delay convergence of the Gauss series, and may also lead to severe cancellation. … The representation (15.6.1) can be used to compute the hypergeometric function in the sector $|\operatorname{ph}\left(1-z\right)|<\pi$. … Initial values for moderate values of $|a|$ and $|b|$ can be obtained by the methods of §15.19(i), and for large values of $|a|$, $|b|$, or $|c|$ via the asymptotic expansions of §§15.12(ii) and 15.12(iii). For example, in the half-plane $\Re z\leq\frac{1}{2}$ we can use (15.12.2) or (15.12.3) to compute $F\left(a,b;c+N+1;z\right)$ and $F\left(a,b;c+N;z\right)$, where $N$ is a large positive integer, and then apply (15.5.18) in the backward direction. …
##### 10: 10.17 Asymptotic Expansions for Large Argument
10.17.4 $Y_{\nu}\left(z\right)\sim\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\*\left(% \sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{a_{2k}(\nu)}{z^{2k}}+\cos\omega\sum% _{k=0}^{\infty}(-1)^{k}\frac{a_{2k+1}(\nu)}{z^{2k+1}}\right),$ $|\operatorname{ph}z|\leq\pi-\delta$,