functions f(ϵ,ℓ;r),h(ϵ,ℓ;r)
(0.020 seconds)
11—20 of 438 matching pages
11: 7.12 Asymptotic Expansions
12: 10 Bessel Functions
Chapter 10 Bessel Functions
…13: 15.1 Special Notation
14: 27.5 Inversion Formulas
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►
27.5.1
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►The set of all number-theoretic functions
with forms an abelian group under Dirichlet multiplication, with the function
in (27.2.5) as identity element; see Apostol (1976, p. 129).
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►
27.5.3
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►
27.5.6
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27.5.8
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15: 7.14 Integrals
16: 7.23 Tables
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►
•
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Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
17: 16.1 Special Notation
…
►The main functions treated in this chapter are the generalized hypergeometric function
, the Appell (two-variable hypergeometric) functions
, , , , and the Meijer -function
.
Alternative notations are , , and for the generalized hypergeometric function, , , , , for the Appell functions, and for the Meijer -function.
18: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►Functions
for which
are
identified with each other. The space
becomes a separable
Hilbert space with inner product
►
1.18.12
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►Spectral expansions of
, and of functions
of
, these being expansions of
and
in terms of the eigenvalues and eigenfunctions summed over the spectrum,
then follow:
…
►where
=
,
being that of (1.8.3) and (1.8.4). The eigenfunction expansions of (1.8.1) and (1.8.2) follow from Cases 1, 2, above.
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►
1.18.47
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19: 33.3 Graphics
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►
§33.3(i) Line Graphs of the Coulomb Radial Functions and
… ►
33.3.1
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►
§33.3(ii) Surfaces of the Coulomb Radial Functions and
…20: 32.14 Combinatorics
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►
32.14.1
►where the distribution function
is defined here by
►
32.14.2
…
►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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