AbstractIn this paper, we consider two types of extended Euler sums:Ep,q(k)=∑n=1∞1nq∑r=1kn1rp,Tp,q(k)=∑n=1∞1nq∑r=1⌊n/k⌋1rp,where ⌊x⌋ is the largest integer ⩽x. In particular, Ep,q(1)=Tp,q(1) are classical Euler sums. We develop a systematic method to evaluate these extended Euler sums as well as their corresponding alternating sums when the weight p+q is odd
AbstractLet sn=1+1/2+⋯+1/(n−1)−logn. In 1995, the author has found a series transformation of the ty...
AbstractIn this paper, some mistakes in the paper which is cited in the title are corrected. Fortuna...
AbstractWe show a limit formula for Eisenstein series by using the theory of a multiple cotangent fu...
AbstractThe Apéry polynomials are given byAn(x)=∑k=0n(nk)2(n+kk)2xk(n=0,1,2,…). (Those An=An(1) are ...
AbstractLet φ(q)=∑n=−∞∞qn2 (|q|<1). For k∈N it is shown that there exist k rational numbers A(k,0),…...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractIn this paper we establish a q-analogue of a congruence of Sun concerning the products of bi...
AbstractWe investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers
AbstractThe sums ∑(l,m)∈N2,l+6m=nσ(l)σ(m) and ∑(l,m)∈N2,2l+3m=nσ(l)σ(m) are evaluated for all n∈N, a...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
AbstractIn this paper we study a two-variable p-adic q–l-function lp,q(s,t|χ) for Dirchlet's charact...
AbstractLet [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine ∑x=1...
AbstractIn this note, we obtain the following identities,∑a+b+c=nζ(2a,2b,2c)=58ζ(2n)−14ζ(2)ζ(2n−2),f...
AbstractWe give a short proof of Miki's identity for Bernoulli numbers,∑i=2n-2βiβn-i-∑i=2n-2niβiβn-i...
In this paper, we establish several new modular equations of degree 9 using Ramanujan's mixed modula...
AbstractLet sn=1+1/2+⋯+1/(n−1)−logn. In 1995, the author has found a series transformation of the ty...
AbstractIn this paper, some mistakes in the paper which is cited in the title are corrected. Fortuna...
AbstractWe show a limit formula for Eisenstein series by using the theory of a multiple cotangent fu...
AbstractThe Apéry polynomials are given byAn(x)=∑k=0n(nk)2(n+kk)2xk(n=0,1,2,…). (Those An=An(1) are ...
AbstractLet φ(q)=∑n=−∞∞qn2 (|q|<1). For k∈N it is shown that there exist k rational numbers A(k,0),…...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractIn this paper we establish a q-analogue of a congruence of Sun concerning the products of bi...
AbstractWe investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers
AbstractThe sums ∑(l,m)∈N2,l+6m=nσ(l)σ(m) and ∑(l,m)∈N2,2l+3m=nσ(l)σ(m) are evaluated for all n∈N, a...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
AbstractIn this paper we study a two-variable p-adic q–l-function lp,q(s,t|χ) for Dirchlet's charact...
AbstractLet [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine ∑x=1...
AbstractIn this note, we obtain the following identities,∑a+b+c=nζ(2a,2b,2c)=58ζ(2n)−14ζ(2)ζ(2n−2),f...
AbstractWe give a short proof of Miki's identity for Bernoulli numbers,∑i=2n-2βiβn-i-∑i=2n-2niβiβn-i...
In this paper, we establish several new modular equations of degree 9 using Ramanujan's mixed modula...
AbstractLet sn=1+1/2+⋯+1/(n−1)−logn. In 1995, the author has found a series transformation of the ty...
AbstractIn this paper, some mistakes in the paper which is cited in the title are corrected. Fortuna...
AbstractWe show a limit formula for Eisenstein series by using the theory of a multiple cotangent fu...
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