limiting forms

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1: 33.18 Limiting Forms for Large $\mathrm{\ell }$

§33.18 Limiting Forms for Large $\mathrm{\ell }$

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2: 10.30 Limiting Forms

§10.30 Limiting Forms

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§10.30(i) $z\to 0$

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3: 26.5 Lattice Paths: Catalan Numbers

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§26.5(iv) Limiting Forms

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4: 33.5 Limiting Forms for Small $\rho$, Small $|\eta |$, or Large $\mathrm{\ell }$

§33.5 Limiting Forms for Small $\rho$, Small $|\eta |$, or Large $\mathrm{\ell }$

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§33.5(i) Small $\rho$

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§33.5(iii) Small $|\eta |$

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§33.5(iv) Large $\mathrm{\ell }$

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5: 10.52 Limiting Forms

§10.52 Limiting Forms

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6: 33.21 Asymptotic Approximations for Large $|r|$

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§33.21(i) Limiting Forms

►We indicate here how to obtain the limiting forms of $f(ϵ,\mathrm{\ell };r)$, $h(ϵ,\mathrm{\ell };r)$, $s(ϵ,\mathrm{\ell };r)$, and $c(ϵ,\mathrm{\ell };r)$ as $r\to \pm \mathrm{\infty }$, with $ϵ$ and $\mathrm{\ell }$ fixed, in the following cases: …

7: 29.5 Special Cases and Limiting Forms

§29.5 Special Cases and Limiting Forms

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8: 18.11 Relations to Other Functions

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§18.11(ii) Formulas of Mehler–Heine Type

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Jacobi

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Laguerre

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Hermite

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9: 11.13 Methods of Computation

… ►Then from the limiting forms for small argument (§§11.2(i), 10.7(i), 10.30(i)), limiting forms for large argument (§§11.6(i), 10.7(ii), 10.30(ii)), and the connection formulas (11.2.5) and (11.2.6), it is seen that ${𝐇}_{\nu }\left(x\right)$ and ${𝐋}_{\nu }\left(x\right)$ can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity. …

10: 33.10 Limiting Forms for Large $\rho$ or Large $\left|\eta \right|$

§33.10 Limiting Forms for Large $\rho$ or Large $\left|\eta \right|$

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§33.10(i) Large $\rho$

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§33.10(ii) Large Positive $\eta$

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§33.10(iii) Large Negative $\eta$

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