Truncated series from the quintuple product identity
نویسندگان
چکیده
منابع مشابه
Finite form of the quintuple product identity
where the q-shifted factorial is defined by (x; q)0 = 1 and (x; q)n = (1− x)(1 − qx) · · · (1− q x) for n = 1, 2, · · · with the following abbreviated multiple parameter notation [α, β, · · · , γ; q]∞ = (α; q)∞(β; q)∞ · · · (γ; q)∞. This identity has several important applications in combinatorial analysis, number theory and special functions. For the historical note, we refer the reader to the...
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The quintuple identity has a long history and, as Berndt [5] points out, it is difficult to assign priority to it. It seems that a proof of the identity was first published in H. A. Schwartz’s book in 1893 [19]. Watson gave a proof in 1929 in his work on the RogersRamanujan continued fractions [20]. Since then, various proofs have appeared. To name a few, Carlitz and Subbarao gave a simple proo...
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In the first part of this paper, series and product representations of four single-variable triple products T0, T1, T2, T3 and four single-variable quintuple products Q0, Q1, Q2, Q3 are defined. Reduced forms and reduction formulas for these eight functions are given, along with formulas which connect them. The second part of the paper contains a systematic computer search for linear trinomial ...
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Knowledge of a truncated Fourier series expansion for a discontinuous 2^-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval [-1, 1], is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree M for the M locations of discontinuities in e...
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Introduction . . . . . . . . . $ 1. The problem . . . . . . . . . $2. Residues of cuspidal Eisenstein series 83. Exponents . . . . . . . . . $4. A comparison between two groups . $5. A property of the truncation operator $6. The constant terms of Eisenstein series $7. The negative dual chamber . . . . $8. Coefficients of the zero exponents . . $9. Conclusion . . . . . . . . . Bibliography . . ....
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.05.013