functions f(ϵ,ℓ;r),h(ϵ,ℓ;r)
(0.022 seconds)
21—30 of 443 matching pages
21: 32.14 Combinatorics
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32.14.1
►where the distribution function
is defined here by
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32.14.2
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►The distribution function
given by (32.14.2) arises in random matrix theory where it gives the limiting distribution for the normalized largest eigenvalue in the Gaussian Unitary Ensemble of Hermitian matrices; see Tracy and Widom (1994).
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22: 33.11 Asymptotic Expansions for Large
23: 27.4 Euler Products and Dirichlet Series
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►Every multiplicative satisfies the identity
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►The completely multiplicative function
gives the Euler product representation of the Riemann zeta function
(§25.2(i)):
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►The Riemann zeta function is the prototype of series of the form
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27.4.4
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►The function
is a generating function, or more precisely, a Dirichlet generating
function, for the coefficients.
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24: Bibliography Q
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Some inequalities of the incomplete gamma and related functions.
Z. Anal. Anwendungen 18 (3), pp. 793–799.
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25: 28.19 Expansions in Series of Functions
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►Let be a normal value (§28.12(i)) with respect to , and be a function that is analytic on a doubly-infinite open strip that contains the real axis.
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28.19.1
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28.19.2
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28.19.3
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26: 33.1 Special Notation
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►The main functions treated in this chapter are first the Coulomb radial functions
, , (Sommerfeld (1928)), which are used in the case of repulsive Coulomb interactions, and secondly the functions
, , , (Seaton (1982, 2002a)), which are used in the case of attractive Coulomb interactions.
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Greene et al. (1979):
, , .
27: 8.14 Integrals
28: 16.2 Definition and Analytic Properties
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§16.2(i) Generalized Hypergeometric Series
… ►Equivalently, the function is denoted by or , and sometimes, for brevity, by . … ►
16.2.3
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16.2.5
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►When and is fixed and not a branch point, any branch of is an entire function of each of the parameters .
29: 33.5 Limiting Forms for Small , Small , or Large
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§33.5(i) Small
… ►§33.5(ii)
… ►For the functions , , , see §§10.47(ii), 10.2(ii). … ►§33.5(iii) Small
… ►§33.5(iv) Large
…30: 33.14 Definitions and Basic Properties
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