Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust ...Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.展开更多
基于正项级数通项的比值 a n+p/ a n ≤ b n+p /b n 的分析,得到了 Kummer 判别法的一种推广形式,进一步给出了其极限表示.对推广的 Kummer 判别法中的赋值,分别得到推广的达朗贝尔判别法,推广的拉贝判别法及推广的贝特朗判别法.类似得...基于正项级数通项的比值 a n+p/ a n ≤ b n+p /b n 的分析,得到了 Kummer 判别法的一种推广形式,进一步给出了其极限表示.对推广的 Kummer 判别法中的赋值,分别得到推广的达朗贝尔判别法,推广的拉贝判别法及推广的贝特朗判别法.类似得到高斯判别法的推广形式.最后通过若干例子验证了方法的有效性.展开更多
The main aim of this paper is to define and study of a new matrix functions, say, the pl(m,n)-Kummer matrix function of two complex variables. The radius of regularity, recurrence relation and several new results on t...The main aim of this paper is to define and study of a new matrix functions, say, the pl(m,n)-Kummer matrix function of two complex variables. The radius of regularity, recurrence relation and several new results on this function are established when the positive integers p is greater than one. Finally, we obtain a higher order partial differential equation satisfied by the pl(m,n)-Kummer matrix function and some special properties.展开更多
Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some genera...Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.展开更多
Let F<sub>q</sub> be a finite field of q elements with characteristic p. Let k=F<sub>q</sub>（T） be a ra-tional function field, and k<sup>ac</sup>, a fixed algebraic closure of k. ...Let F<sub>q</sub> be a finite field of q elements with characteristic p. Let k=F<sub>q</sub>（T） be a ra-tional function field, and k<sup>ac</sup>, a fixed algebraic closure of k. Let M be a monic polynomialin R=F<sub>q</sub>[T]. The Carlitz action of M on a∈k<sup>ac</sup> is defined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
文摘Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.
文摘基于正项级数通项的比值 a n+p/ a n ≤ b n+p /b n 的分析,得到了 Kummer 判别法的一种推广形式,进一步给出了其极限表示.对推广的 Kummer 判别法中的赋值,分别得到推广的达朗贝尔判别法,推广的拉贝判别法及推广的贝特朗判别法.类似得到高斯判别法的推广形式.最后通过若干例子验证了方法的有效性.
文摘The main aim of this paper is to define and study of a new matrix functions, say, the pl(m,n)-Kummer matrix function of two complex variables. The radius of regularity, recurrence relation and several new results on this function are established when the positive integers p is greater than one. Finally, we obtain a higher order partial differential equation satisfied by the pl(m,n)-Kummer matrix function and some special properties.
基金Supported by National Natural Science Foundation of China(Grant No.10601039)
文摘Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.
文摘Let F<sub>q</sub> be a finite field of q elements with characteristic p. Let k=F<sub>q</sub>（T） be a ra-tional function field, and k<sup>ac</sup>, a fixed algebraic closure of k. Let M be a monic polynomialin R=F<sub>q</sub>[T]. The Carlitz action of M on a∈k<sup>ac</sup> is defined
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.
