- Full text PDF available (13)
- This year (0)
- Last 5 years (6)
- Last 10 years (8)
Let λ = (λ1, · · · , λm) be a partition of k. Let r λ (n) denote the number of solutions in integers of λ1x 2 1 + · · · + λmx 2 m = n, and let t λ (n) denote the number of solutions in non negative integers of λ1x1(x1 + 1)/2 + · · · + λmxm(xm + 1)/2 = n. We prove that if 1 ≤ k ≤ 7, then there is a constant c λ , depending only on λ, such that r λ (8n + k) =… (More)
In this paper we establish some upper bounds for the largest of minimum degree eigenvalues and a lower bound for the largest of minimum degree eigenvalues of trees.
In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bound obtained by Beineke and Hegde .
The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the… (More)
In this paper we give two integral representations for the Ramanujan's cubic continued fraction V (q) and also derive a modular equation relating V (q) and V (q 3). We also establish some modular equations and a transformation formula for Ra-manujan's theta-function. As an application of these, we compute several new explicit evaluations of theta-functions… (More)
Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan's forty… (More)
In this paper, we obtain some new transformation formulas for Ramanujan's 1 ψ 1 summation formula and also establish some eta-function identities. We also deduce a q-gamma function identity, an q-integral and some interesting series representations for π 3/2 2 √ 2Γ 2 (3/4) and the beta function B(x, y) .
In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bounds given by Beineke and Hegde  and Adiga, Ramaswamy and Somashekara , for n ≥ 28.
In a manuscript of Ramanujan, published with his Lost Notebook  there are forty identities involving the Rogers-Ramanujan functions. In this paper, we establish several modular relations involving the Rogers-Ramanujan functions and the Rogers-Ramanujan-Slater type functions of order fifteen which are analogues to Ramanujan's well known forty identities.… (More)