In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and dedu...In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases.展开更多
In this paper, we observe the generalized Harmonic numbers H<sub>n,k,r</sub> (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers H<sub>n,k,r&...In this paper, we observe the generalized Harmonic numbers H<sub>n,k,r</sub> (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers H<sub>n,k,r</sub> (α,β) with Changhee sequences, Daehee sequences, Degenerate Changhee-Genoocchi sequences, Two kinds of degenerate Stirling numbers. Using Riordan arrays, we explore interesting relations between these polynomials, Apostol Bernoulli sequences, Apostol Euler sequences, Apostol Genoocchi sequences.展开更多
In this paper,the expressions of two classes of infinite series in terms of finite series involving Bernoulli numbers are obtained.As applications,we derive some special series including Dirichlet beta functionβ(s)wi...In this paper,the expressions of two classes of infinite series in terms of finite series involving Bernoulli numbers are obtained.As applications,we derive some special series including Dirichlet beta functionβ(s)with argument 2n+1 and Dirichlet lambda functionλ(s)with argument 2n.In addition,we solve the problem proposed recently by Zhou(2021).展开更多
The aim of this paper is to give some analytic functions which are related to the generating functions for the central factorial numbers. By using these functions and p-adic Volkenborn integral, we derive many new ide...The aim of this paper is to give some analytic functions which are related to the generating functions for the central factorial numbers. By using these functions and p-adic Volkenborn integral, we derive many new identities associated with the Bernoulli and Euler numbers, the central factorial numbers and the Stirling numbers. We also give some remarks and comments on these analytic functions, which are related to the generating functions for the special numbers.展开更多
We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient p...We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient power, namely to the third power of the Fermat quotient. Using this result and the Gessel identity (2005) combined with our past work (2021), we are able to relate residues of some truncated convolutions of Bernoulli numbers with some Ernvall-Metsänkyla residues to residues of some full convolutions of the same kind. We also establish some congruences concerning other related weighted sums of powers of integers when these sums are weighted by some analogs of the Teichmüller characters.展开更多
基金Supported by the PCSIRT of Education of China(IRT0621)Supported by the Innovation Program of Shanghai Municipal Education Committee of China(08ZZ24)Supported by the Henan Innovation Project for University Prominent Research Talents of China(2007KYCX0021)
文摘In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases.
文摘In this paper, we observe the generalized Harmonic numbers H<sub>n,k,r</sub> (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers H<sub>n,k,r</sub> (α,β) with Changhee sequences, Daehee sequences, Degenerate Changhee-Genoocchi sequences, Two kinds of degenerate Stirling numbers. Using Riordan arrays, we explore interesting relations between these polynomials, Apostol Bernoulli sequences, Apostol Euler sequences, Apostol Genoocchi sequences.
文摘In this paper,the expressions of two classes of infinite series in terms of finite series involving Bernoulli numbers are obtained.As applications,we derive some special series including Dirichlet beta functionβ(s)with argument 2n+1 and Dirichlet lambda functionλ(s)with argument 2n.In addition,we solve the problem proposed recently by Zhou(2021).
文摘The aim of this paper is to give some analytic functions which are related to the generating functions for the central factorial numbers. By using these functions and p-adic Volkenborn integral, we derive many new identities associated with the Bernoulli and Euler numbers, the central factorial numbers and the Stirling numbers. We also give some remarks and comments on these analytic functions, which are related to the generating functions for the special numbers.
文摘We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient power, namely to the third power of the Fermat quotient. Using this result and the Gessel identity (2005) combined with our past work (2021), we are able to relate residues of some truncated convolutions of Bernoulli numbers with some Ernvall-Metsänkyla residues to residues of some full convolutions of the same kind. We also establish some congruences concerning other related weighted sums of powers of integers when these sums are weighted by some analogs of the Teichmüller characters.
