Lebesgue%20constants
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21: 1.17 Integral and Series Representations of the Dirac Delta
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►The last condition is satisfied, for example, when as , where is a real constant.
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►In the language of physics and applied mathematics, these equations indicate the normalizations chosen for these non- improper eigenfunctions of the differential operators (with derivatives respect to spatial co-ordinates) which generate them; the normalizations (1.17.12_1) and (1.17.12_2) are explicitly derived in Friedman (1990, Ch. 4), the others follow similarly.
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22: 8 Incomplete Gamma and Related
Functions
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23: 28 Mathieu Functions and Hill’s Equation
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24: 2.5 Mellin Transform Methods
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►(The last order estimate follows from the Riemann–Lebesgue lemma, §1.8(i).)
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►where () is an arbitrary integer and is an arbitrary small positive constant.
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►where .
…where is Euler’s constant (§5.2(ii)).
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25: 23 Weierstrass Elliptic and Modular
Functions
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26: 1.5 Calculus of Two or More Variables
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►that is, for every arbitrarily small positive constant
there exists () such that
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►In particular, and can be constants.
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►Moreover, if are finite or infinite constants and is piecewise continuous on the set , then
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►A more general concept of integrability (both finite and infinite) for functions on domains in is Lebesgue integrability.
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27: 36.5 Stokes Sets
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►where denotes a real critical point (36.4.1) or (36.4.2), and denotes a critical point with complex or , connected with by a steepest-descent path (that is, a path where ) in complex or space.
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36.5.4
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36.5.7
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28: 11.6 Asymptotic Expansions
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11.6.1
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►where is an arbitrary small positive constant.
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11.6.2
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►where is Euler’s constant (§5.2(ii)).
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29: 5.11 Asymptotic Expansions
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►The scaled gamma function is defined in (5.11.3) and its main property is as in the sector .
Wrench (1968) gives exact values of up to .
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►In this subsection , , and are real or complex constants.
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5.11.12
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5.11.19
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