odd part
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1: 26.21 Tables
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►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts
, partitions into parts
, and unrestricted plane partitions up to 100.
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2: 1.12 Continued Fractions
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►If , , then is called the odd part of .
The odd part of exists iff , , and up to equivalence is given by
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►and the even and odd parts of the continued fraction converge to finite values.
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3: 26.10 Integer Partitions: Other Restrictions
4: 28.23 Expansions in Series of Bessel Functions
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►When the series in the even-numbered equations converge for and , and the series in the odd-numbered equations converge for and .
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5: 18.17 Integrals
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►
18.17.41
. Also, , even;
,
odd.
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6: 9.13 Generalized Airy Functions
7: 23.15 Definitions
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►In §§23.15–23.19, and
denote the Jacobi modulus and complementary modulus, respectively, and () denotes the nome; compare §§20.1 and 22.1.
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►A modular function
is a function of that is meromorphic in the half-plane , and has the property that for all , or for all belonging to a subgroup of SL,
►
23.15.5
,
►where is a constant depending only on , and (the level) is an integer or half an odd integer.
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8: 37.15 Orthogonal Polynomials on the Ball
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►
37.15.21
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9: 20.2 Definitions and Periodic Properties
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►For fixed , each is an entire function of with period ; is odd in and the others are even.
For fixed , each of , , , and is an analytic function of for , with a natural boundary , and correspondingly, an analytic function of for with a natural boundary .
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