# limit relations

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##### 4: 18.19 Hahn Class: Definitions
In addition to the limit relations in §18.7(iii) there are limit relations involving the further families in the Askey scheme, see §§18.21(ii) and 18.26(ii). …
##### 7: 17.4 Basic Hypergeometric Functions
17.4.2 $\lim_{q\to 1-}{{}_{r+1}\phi_{s}}\left({q^{a_{0}},q^{a_{1}},\dots,q^{a_{r}}% \atop q^{b_{1}},\dots,q^{b_{s}}};q,(q-1)^{s-r}z\right)={{}_{r+1}F_{s}}\left({a% _{0},a_{1},\dots,a_{r}\atop b_{1},\dots,b_{s}};z\right).$
##### 8: Bibliography C
• F. Calogero (1978) Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial ${L}_{n}^{\alpha}(x)$ as the index $\alpha\rightarrow\infty$ and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials. Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.
• ##### 9: Errata
• Equation (17.4.2)
17.4.2 $\lim_{q\to 1-}{{}_{r+1}\phi_{s}}\left({q^{a_{0}},q^{a_{1}},\dots,q^{a_{r}}% \atop q^{b_{1}},\dots,q^{b_{s}}};q,(q-1)^{s-r}z\right)={{}_{r+1}F_{s}}\left({a% _{0},a_{1},\dots,a_{r}\atop b_{1},\dots,b_{s}};z\right)$

This limit relation, which was previously accurate for ${{}_{r+1}\phi_{r}}$, has been updated to be accurate for ${{}_{r+1}\phi_{s}}$.

• ##### 10: 28.34 Methods of Computation
• (b)

Representations for $w_{\mbox{\tiny I}}(\pi;a,\pm q)$ with limit formulas for special solutions of the recurrence relations §28.4(ii) for fixed $a$ and $q$; see Schäfke (1961a).