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1: 33.18 Limiting Forms for Large
§33.18 Limiting Forms for Large
2: 10.30 Limiting Forms
§10.30 Limiting Forms
§10.30(i) z 0
3: 26.5 Lattice Paths: Catalan Numbers
§26.5(iv) Limiting Forms
4: 33.5 Limiting Forms for Small ρ , Small | η | , or Large
§33.5 Limiting Forms for Small ρ , Small | η | , or Large
§33.5(i) Small ρ
§33.5(iii) Small | η |
§33.5(iv) Large
5: 33.21 Asymptotic Approximations for Large | r |
§33.21(i) Limiting Forms
We indicate here how to obtain the limiting forms of f ( ϵ , ; r ) , h ( ϵ , ; r ) , s ( ϵ , ; r ) , and c ( ϵ , ; r ) as r ± , with ϵ and fixed, in the following cases: …
6: 29.5 Special Cases and Limiting Forms
§29.5 Special Cases and Limiting Forms
7: 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 ν ( x ) and L ν ( x ) can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity. …
8: 18.11 Relations to Other Functions
§18.11(ii) Formulas of Mehler–Heine Type
Jacobi
Laguerre
Hermite
9: 33.10 Limiting Forms for Large ρ or Large | η |
§33.10 Limiting Forms for Large ρ or Large | η |
§33.10(i) Large ρ
§33.10(ii) Large Positive η
§33.10(iii) Large Negative η
10: 22.5 Special Values
§22.5(ii) Limiting Values of k
Table 22.5.3: Limiting forms of Jacobian elliptic functions as k 0 .
sn ( z , k ) sin z cd ( z , k ) cos z dc ( z , k ) sec z ns ( z , k ) csc z
Table 22.5.4: Limiting forms of Jacobian elliptic functions as k 1 .
sn ( z , k ) tanh z cd ( z , k ) 1 dc ( z , k ) 1 ns ( z , k ) coth z