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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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“Approximation by tangents”

8.45211 For large values of the index (where the argument is less than the index).

Suppose that x < 0 and ν < 0. Let us set ν/x = cosh α. Then, for large values of ν, the following expansions are valid:

1. 

Jv(vcoshα)~exp(vtanhαvα)2vπtanhα{1+1v(18cothα524coth3α)+1v2(9128coth2α231576coth4α+11553456coth6α)+}

si823_e  WA 269(3)

2. 

Yv(vcoshα)~exp(vαvtanhα)π2vtanhα{1+1v(18cothα524coth3α)+1v2(9128coth2α231576coth4α+11553456coth6α)+}

si824_e  WA 270(5)

8.453 For large values of the index (where the argument is greater than ...

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