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asymptotic forms for small q

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1: 28.15 Expansions for Small q
§28.15 Expansions for Small q
2: 28.4 Fourier Series
§28.4(vi) Behavior for Small q
3: 28.20 Definitions and Basic Properties
with its algebraic form
28.20.5 Me ν ( z , q ) = me ν ( - i z , q ) ,
§28.20(iii) Solutions M ν ( j )
Assume first that ν is real, q is positive, and a = λ ν ( q ) ; see §28.12(i). …Then from §2.7(ii) it is seen that equation (28.20.2) has independent and unique solutions that are asymptotic to ζ 1 / 2 e ± 2 i h ζ as ζ in the respective sectors | ph ( i ζ ) | 3 2 π - δ , δ being an arbitrary small positive constant. …