Results 281 to 290 of about 58,299 (310)

Best Summation Formulae and Discrete Splines

SIAM Journal on Numerical Analysis, 1973
The problem of obtaining a best summation formula for a finite sequence of real numbers in terms of a fixed number of terms of the sequence is reduced to a solvable linear or quadratic programming problem. This is done by developing the appropriate discrete Taylor and Peano theorems.
Mangasarian, O. L., Schumaker, L. L.
openaire   +2 more sources

Some summation formula

Moscow University Mathematics Bulletin, 2011
An analogue of Euler’s summation formula over integer points of an arbitrary interval is obtained in the paper.
openaire   +1 more source

An Euler Summation Formula

The American Mathematical Monthly, 1936
(1936). An Euler Summation Formula. The American Mathematical Monthly: Vol. 43, No. 1, pp. 9-21.
openaire   +1 more source

Summation Formulas Involving Polynomials

The Mathematics Teacher, 2015
Direct proofs for the sum of squares, the sum of cubes, and the sum of fourth powers use visualization to teach the identities.
openaire   +1 more source

Some Cubic Summation and Transformation Formulas

The Ramanujan Journal, 1997
This informative paper deals with the basic analogous of two summation formulas and a cubic transformation formula involving Gaussian hypergeometric function \(_2F_1\). The author uses the \(q\)-binomial formula in the base \(q^3\) and certain known series manipulative techniques to obtain his interesting results.
openaire   +1 more source

Summation Formulas for Basic Hypergeometric Series

SIAM Journal on Mathematical Analysis, 1981
Summation formulas for basic hypergeometric series are derived which are q-analogues of Minton’s [J. Math. Phys., 11 (1970), pp. 1375–1376] and Karlsson’s [J. Math. Phys., 12 (1971), pp. 270–271] summation formulas for generalized hypergeometric series, and some interesting limit cases are considered.
openaire   +1 more source

Closed-Form Summation Formulae

2017
Closed-form summation formulae provide a compact means of describing different types of spectra. By combining a limited number of sinusoids, we can generate complex waveforms with many harmonic or inharmonic partials. In this chapter, we will look at various formulae, and their implementation and application, from band-limited pulse oscillators to ...
openaire   +1 more source

Appendix C: Summation Formulae

2012
In this appendix, summation formulae for series involving nested sums and binomial coefficients are presented. Some of them are used in this book. These series have a canonical form, in the sense that the argument of a nested sum \(S_k\) is \(n-1\), there are powers of \(1/n^j\) etc.
openaire   +1 more source

Summation formulas

2023
openaire   +1 more source

VORONOÏ'S SUMMATION FORMULA

The Quarterly Journal of Mathematics, 1932
openaire   +1 more source