limiting forms as trigonometric functions
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1: 18.11 Relations to Other Functions
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Hermite
…2: 22.5 Special Values
§22.5 Special Values
… ►For the other nine functions ratios can be taken; compare (22.2.10). … ►§22.5(ii) Limiting Values of
… ►In these cases the elliptic functions degenerate into elementary trigonometric and hyperbolic functions, respectively. … ►3: 33.10 Limiting Forms for Large or Large
§33.10 Limiting Forms for Large or Large
►§33.10(i) Large
… ►§33.10(ii) Large Positive
… ►§33.10(iii) Large Negative
…4: 10.45 Functions of Imaginary Order
§10.45 Functions of Imaginary Order
… ►In consequence of (10.45.5)–(10.45.7), and comprise a numerically satisfactory pair of solutions of (10.45.1) when is large, and either and , or and , comprise a numerically satisfactory pair when is small, depending whether or . … ►In this reference is denoted by . …5: 10.24 Functions of Imaginary Order
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6: 10.28 Wronskians and Cross-Products
7: 11.9 Lommel Functions
§11.9 Lommel Functions
… ►The inhomogeneous Bessel differential equation … ►the right-hand side being replaced by its limiting form when is an odd negative integer. … ► … ►8: 10.5 Wronskians and Cross-Products
9: 6.2 Definitions and Interrelations
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►This is also true of the functions
and defined in §6.2(ii).
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►The logarithmic integral is defined by
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is an odd entire function.
… is an even entire function.
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