Kim, Aeran
(2014)
*Applications to the Quadratic Forms and Product-to-sum Formulae.*
British Journal of Mathematics & Computer Science, 4 (10).
pp. 1335-1350.
ISSN 22310851

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Official URL: https://doi.org/10.9734/BJMCS/2014/8683

## Abstract

In this paper, we attempt to express two valuesG(q) :=∞∑n=1g(n)qn= 24q∞∏n=1(1 +qn)32(1−qn)16(1 +q2n)12,H(q) :=∞∑n=1h(n)qn= 212q3∞∏n=1(1 +q2n)4(1−q4n)16into sums of squares and obtaing(n) = 8∑(x1,x2,···,x11,x12)∈Z12x21+x22+···+x29+x210+2(x211+x212)=n(x210−2x212),h(n) = 1024∑(x1,x2,x3,x4)∈Z42(x21+x22+2x24)+x23=n(−1)x21+x22+1(x41−3x21x22)(x23−4x24)(see Theorem 1.1 and Theorem 1.2, respectively). Finally, we obtain some relationsφ1(q)according toξ1(q),φ(q), andψ(q).

Item Type: | Article |
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Subjects: | Opene Prints > Mathematical Science |

Depositing User: | Managing Editor |

Date Deposited: | 17 Jun 2023 13:02 |

Last Modified: | 12 Jan 2024 06:59 |

URI: | http://geographical.go2journals.com/id/eprint/2210 |