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Search: id:A053252
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| A053252 |
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Coefficients of the '3rd order' mock theta function chi(q). |
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+0
8
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| 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, -1, 0, 1, 1, 1, -1, 0, 0, 0, 1, 0, 0, -1, 0, 1, 1, 1, 0, -1, -1, 1, 1, 0, -1, -1, 0, 1, 2, 1, -1, -1, 0, 1, 1, 0, -1, -2, 0, 1, 2, 1, -1, -1, -1, 1, 2, 1, -1, -2, -1, 2, 2, 1, -1, -2, -1, 1, 2, 0, -1, -3, 0, 2, 3, 2, -2, -2, -1, 2, 3, 0, -2, -3, -1, 2, 3, 2, -3, -3, -1, 2, 4, 1, -2, -4, -1, 3, 4, 2, -2, -4
(list; graph; listen)
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OFFSET
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0,38
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REFERENCES
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Leila A. Dragonette, Some asymptotic formulae for the mock theta functions of Ramanujan, Trans. Amer. Math. Soc., 72 (1952) 474-500.
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 55, Eq. (26.14).
Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355.
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 17.
George N. Watson, The final problem: an account of the mock theta functions, J. London Math. Soc., 11 (1936) 55-80.
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FORMULA
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G.f.: chi(q) = sum for n >= 0 of q^n^2/((1-q+q^2)(1-q^2+q^4)...(1-q^n+q^(2n))).
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MATHEMATICA
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Series[Sum[q^n^2/Product[1-q^k+q^(2k), {k, 1, n}], {n, 0, 10}], {q, 0, 100}]
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CROSSREFS
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Other '3rd order' mock theta functions are at A000025, A053250, A053251, A053253, A053254, A053255.
Sequence in context: A106276 A037907 A037801 this_sequence A117195 A107034 A117410
Adjacent sequences: A053249 A053250 A053251 this_sequence A053253 A053254 A053255
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KEYWORD
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sign,easy
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AUTHOR
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Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 19 1999
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