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
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.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
设a,b为整数,b≠0。广义Fibonacci序列{un}定义为u0=0,u1=1,un+2=aun+1+bun(n≥0)。设a,b,c,n,k,m,r为整数,求解关于t1,…,tm-r的不定方程(+1-)1m ri i k m ii?t e u c=∑=(k>0,m-1>r≥0,c∈Z,ei=±1,i=1,…,m-r)给出了求解例...设a,b为整数,b≠0。广义Fibonacci序列{un}定义为u0=0,u1=1,un+2=aun+1+bun(n≥0)。设a,b,c,n,k,m,r为整数,求解关于t1,…,tm-r的不定方程(+1-)1m ri i k m ii?t e u c=∑=(k>0,m-1>r≥0,c∈Z,ei=±1,i=1,…,m-r)给出了求解例子,并较详细说明了在构造F-L恒等式方面的应用。展开更多
In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithm...In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.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.
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
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).
文摘设a,b为整数,b≠0。广义Fibonacci序列{un}定义为u0=0,u1=1,un+2=aun+1+bun(n≥0)。设a,b,c,n,k,m,r为整数,求解关于t1,…,tm-r的不定方程(+1-)1m ri i k m ii?t e u c=∑=(k>0,m-1>r≥0,c∈Z,ei=±1,i=1,…,m-r)给出了求解例子,并较详细说明了在构造F-L恒等式方面的应用。
基金partially supported by the National Nature Science Foundation of China(12061033)。
文摘In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.
