Recently in [1] Goyal and Agarwal interpreted a generalized basic series as a generating function for a colour partition function and a weighted lattice path function. This led to an infinite family of combinatorial i...Recently in [1] Goyal and Agarwal interpreted a generalized basic series as a generating function for a colour partition function and a weighted lattice path function. This led to an infinite family of combinatorial identities. Using Frobenius partitions, we in this paper extend the result of [1] and obtain an infinite family of 3-way combinatorial identities. We illustrate by an example that our main result has a potential of yielding Rogers-Ramanujan-MacMahon type identities with convolution property.展开更多
In 1973, Gould and Hsu proved an important reciprocal theorem. The inverse relations determined by the theorem are useful in combinatorial computation, proof of identities and interpolation process. In the present not...In 1973, Gould and Hsu proved an important reciprocal theorem. The inverse relations determined by the theorem are useful in combinatorial computation, proof of identities and interpolation process. In the present note, we shall establish the multivariate ver-展开更多
In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers...In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.展开更多
文摘Recently in [1] Goyal and Agarwal interpreted a generalized basic series as a generating function for a colour partition function and a weighted lattice path function. This led to an infinite family of combinatorial identities. Using Frobenius partitions, we in this paper extend the result of [1] and obtain an infinite family of 3-way combinatorial identities. We illustrate by an example that our main result has a potential of yielding Rogers-Ramanujan-MacMahon type identities with convolution property.
文摘In 1973, Gould and Hsu proved an important reciprocal theorem. The inverse relations determined by the theorem are useful in combinatorial computation, proof of identities and interpolation process. In the present note, we shall establish the multivariate ver-
基金Supported by the National Natural Science Foundation of China(Grant No.11326050)
文摘In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.
