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… ►The symbol may be defined either in terms of symbols or equivalently in terms of symbols: ►
34.6.1… ►The symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments. …
2: 15.15 Sums
… ►For compendia of finite sums and infinite series involving hypergeometric functions see Prudnikov et al. (1990, §§5.3 and 6.7) and Hansen (1975). …
… ►When both conditions are satisfied the symbol can be expressed as the finite sum … ►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).
§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).
7: 5.16 Sums
… ►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).
§1.7(i) Finite Sums…
Finite-sum rules for Macdonald’s functions and Hankel’s symbols.
Integral Transform. Spec. Funct. 10 (2), pp. 115–124.
… ►Every function periodic (mod ) can be expressed as a finite Fourier series of the form …An example is Ramanujan’s sum: … ►is a periodic function of and has the finite Fourier-series expansion … ► is separable for some if … ►The finite Fourier expansion of a primitive Dirichlet character has the form …