of integers
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11—20 of 562 matching pages
11: 26.3 Lattice Paths: Binomial Coefficients
12: 21.6 Products
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21.6.1
►that is, is the set of all matrices that are obtained by premultiplying by any matrix with integer elements; two such matrices in are considered equivalent if their difference is a matrix with integer elements.
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21.6.2
►that is, is the number of elements in the set containing all -dimensional vectors obtained by multiplying on the right by a vector with integer elements.
Two such vectors are considered equivalent if their difference is a vector with integer elements.
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13: 34.5 Basic Properties: Symbol
14: 29.15 Fourier Series and Chebyshev Series
15: 24.14 Sums
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►In the following two identities, valid for , the sums are taken over all nonnegative integers
with .
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24.14.8
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24.14.9
►In the next identity, valid for , the sum is taken over all positive integers
with .
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24.14.10
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16: 26.8 Set Partitions: Stirling Numbers
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►where the summation is over all nonnegative integers
such that
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26.8.20
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26.8.21
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26.8.24
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26.8.25
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17: 27.10 Periodic Number-Theoretic Functions
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►If is a fixed positive integer, then a number-theoretic function is periodic (mod ) if
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27.10.1
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27.10.2
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27.10.5
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27.10.6
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18: 23.18 Modular Transformations
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►Here e and o are generic symbols for even and odd integers, respectively.
In particular, if , and are all even, then
…and is a cusp form of level zero for the corresponding subgroup of SL.
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is a modular form of level zero for SL.
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23.18.6
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19: 27.3 Multiplicative Properties
20: 23.15 Definitions
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►in which are integers, with
…The set of all bilinear transformations of this form is denoted by SL (Serre (1973, p. 77)).
►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,
…where is a constant depending only on , and (the level) is an integer or half an odd integer.
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