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Search: id:A053269
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| A053269 |
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Coefficients of the '6th order' mock theta function psi(q) |
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+0
7
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| 0, 1, -1, 1, -2, 3, -2, 2, -4, 5, -5, 5, -7, 9, -8, 9, -12, 14, -15, 16, -20, 23, -23, 25, -31, 36, -37, 40, -47, 54, -56, 60, -71, 79, -84, 91, -103, 115, -121, 131, -149, 164, -174, 188, -210, 232, -245, 264, -294, 321, -343, 368, -406, 443, -470, 505, -554, 602, -641, 687, -751, 813, -863, 925
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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George E. Andrews and Dean Hickerson, Ramanujan's "lost" notebook VII: The sixth order mock theta functions, Advances in Mathematics, 89 (1991) 60-105
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 4, 13
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FORMULA
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G.f.: psi(q) = sum for n >= 0 of (-1)^n q^(n+1)^2 (1-q)(1-q^3)...(1-q^(2n-1))/((1+q)(1+q^2)...(1+q^(2n+1)))
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MATHEMATICA
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Series[Sum[(-1)^n q^(n+1)^2 Product[1-q^k, {k, 1, 2n-1, 2}]/Product[1+q^k, {k, 1, 2n+1}], {n, 0, 9}], {q, 0, 100}]
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CROSSREFS
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Other '6th order' mock theta functions are at A053268, A053270, A053271, A053272, A053273, A053274, A053275, A053276.
Sequence in context: A098534 A002307 A029247 this_sequence A118665 A027746 A128651
Adjacent sequences: A053266 A053267 A053268 this_sequence A053270 A053271 A053272
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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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