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Some generalizations of Knopp's identity*

✍ Scribed by Huaning Liu

Publisher
Springer
Year
2007
Tongue
English
Weight
101 KB
Volume
38
Category
Article
ISSN
1678-7714

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πŸ“œ SIMILAR VOLUMES

Generalizations of Knopp's Identity
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For integers a; b and n > 0 we define S G Γ°a; b; nÞ ΒΌ X nΓ€1 rΒΌ0 n[br ar n ln G br n and T G Γ°a; b; nÞ ΒΌ X nΓ€1 rΒΌ0 n[br ar n G 0 Γ°fbr=ngÞ GΓ°fbr=ngÞ ; which are similar to the homogeneous Dedekind sum SΓ°a; b; nÞ: In this paper we establish functional equations for S G and T G : Moreover, by means of u

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A remarkably simple proof is presented for an interesting generalization of a combinatorial identity given recently by L. Vietoris [Monatsh. Math. 97 (1984) 157-160]. It is also shown how this general result can be extended further to hold true for basic (or q-) series.

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A generalized q-binomial Vandermonde convolution of Sulanke is proved using a generalization of the Durfee square of a partition. Bender [4] proved the following generalization of the q-binomial Vandermonde convolution: where for l~ O, Bender's identity was generalized by Evans [5], who Obtained a f