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21: 19.10 Relations to Other Functions
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►In each case when , the quantity multiplying supplies the asymptotic behavior of the left-hand side as the left-hand side tends to 0.
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§19.10(ii) Elementary Functions
… ►22: 15.8 Transformations of Variable
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►In (15.8.8) when is a nonpositive integer is interpreted as .
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►Alternatively, if is a negative integer, then we interchange and in .
►In a similar way, when is an integer limits are taken in (15.8.4) and (15.8.5) as follows.
►If is a nonnegative integer, then
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►Lastly, if is a negative integer, then we first apply the transformation
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23: 10.13 Other Differential Equations
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10.13.1
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10.13.2
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10.13.3
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10.13.5
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►In (10.13.9)–(10.13.11) , are any cylinder functions of orders , respectively, and .
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24: 15.3 Graphics
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25: 15.15 Sums
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15.15.1
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26: 17.13 Integrals
27: 15.6 Integral Representations
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►The function (not ) has the following integral representations:
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15.6.1
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15.6.2
; , .
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►In (15.6.2) the point lies outside the integration contour, and assume their principal values where the contour cuts the interval , and at .
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►In (15.6.7) the integration contour separates the poles of and from those of and , and has its principal value.
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28: 15.4 Special Cases
29: 23.18 Modular Transformations
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►according as the elements of in (23.15.3) have the respective forms
…In particular, if , and are all even, then
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23.18.6
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23.18.7
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►Here is a Dedekind sum.
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