finite sum
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1: 34.6 Definition: Symbol
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►The symbol may be defined either in terms of symbols or equivalently in terms of symbols:
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34.6.1
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►The symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments.
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2: 15.15 Sums
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►For compendia of finite sums and infinite series involving hypergeometric functions see Prudnikov et al. (1990, §§5.3 and 6.7) and Hansen (1975).
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3: 34.2 Definition: Symbol
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►When both conditions are satisfied the symbol can be expressed as the finite sum
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►where is defined as in §16.2.
►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§8.21, 8.24–8.26).
4: 34.4 Definition: Symbol
§34.4 Definition: Symbol
… ►The symbol can be expressed as the finite sum … ►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).5: 25.16 Mathematical Applications
6: 5.16 Sums
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►For related sums involving finite field analogs of the gamma and beta functions (Gauss and Jacobi sums) see Andrews et al. (1999, Chapter 1) and Terras (1999, pp. 90, 149).
7: 1.7 Inequalities
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§1.7(i) Finite Sums
…8: Bibliography R
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Finite-sum rules for Macdonald’s functions and Hankel’s symbols.
Integral Transform. Spec. Funct. 10 (2), pp. 115–124.
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9: 27.10 Periodic Number-Theoretic Functions
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►Every function periodic (mod ) can be expressed as a finite Fourier
series of the form
…An example is Ramanujan’s sum:
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►is a periodic function of and has the finite Fourier-series expansion
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is separable for some if
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►The finite Fourier expansion of a primitive Dirichlet character has the form
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10: 25.15 Dirichlet -functions
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25.15.3
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