Some Generalized Formula For Sums of Cube

A Stationary Phase Formula for Generalized Exponential Sums

This paper gives a formula for Generalized Exponential sums which depends entirely upon the singularities mod p, similar to the purpose of the Stationary Phase Formula for Igusa Local Zeta Functions. This new formula is then applied to two examples: strongly non-degenerate homogeneous polynomials and general quadratic polynomials. This work was completed as part of the Mount Holyoke Summer Math...

THE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-k PELL NUMBERS

In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the generalized order-k Pell numbers.

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

The Binet formula, sums and representations of generalized Fibonacci p-numbers

In this paper, we consider the generalized Fibonacci p-numbers and then we give the generalized Binet formula, sums, combinatorial representations and generating function of the generalized Fibonacci p-numbers. Also, using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers. c © 2007 Elsevier Ltd. All rights reserved.

Generalized Eulerian sums

In this note, we derive a number of symmetrical sums involving Eulerian numbers and some of their generalizations. These extend earlier identities of Don Knuth and the authors, and also include several q-nomial sums inspired by recent work of Shareshian and Wachs on the joint distribution of various permutation statistics, such as the number of excedances, the major index and the number of fixe...