elliptic-function form
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21: 26.3 Lattice Paths: Binomial Coefficients
22: 6.7 Integral Representations
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6.7.1
, ,
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6.7.3
, ,
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6.7.4
, .
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6.7.5
, ,
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►Many integrals with exponentials and rational functions, for example, integrals of the type , where is an arbitrary rational function, can be represented in finite form in terms of the function
and elementary functions; see Lebedev (1965, p. 42).
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23: 23.15 Definitions
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►The set of all bilinear transformations of this form is denoted by SL (Serre (1973, p. 77)).
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►If, as a function of , is analytic at , then is called a modular form.
If, in addition, as , then is called a cusp form.
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24: 28.8 Asymptotic Expansions for Large
25: 15.11 Riemann’s Differential Equation
§15.11 Riemann’s Differential Equation
… ►The most general form is given by … ►A conformal mapping of the extended complex plane onto itself has the form … ►for arbitrary and .26: 29.5 Special Cases and Limiting Forms
§29.5 Special Cases and Limiting Forms
…27: 23.18 Modular Transformations
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►according as the elements of in (23.15.3) have the respective forms
…and is a cusp form of level zero for the corresponding subgroup of SL.
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is a modular form of level zero for SL.
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28: 31.14 General Fuchsian Equation
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Normal Form
…29: 33.21 Asymptotic Approximations for Large
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§33.21(i) Limiting Forms
►We indicate here how to obtain the limiting forms of , , , and as , with and fixed, in the following cases: …30: Guide to Searching the DLMF
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►To recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form.
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►Note that the first form may match other functions
than the Bessel
function, so if you are sure you want Bessel , you might as well enter one of the other 3 forms.
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