# The independent derivations by Leonhard Euler and Colin MacLaurin of the Euler-MacLaurin Summation Formula

@article{Mills1985TheID, title={The independent derivations by Leonhard Euler and Colin MacLaurin of the Euler-MacLaurin Summation Formula}, author={Stella Mills}, journal={Archive for History of Exact Sciences}, year={1985}, volume={33}, pages={1-13} }

#### 25 Citations

Euler–Maclaurin expansions without analytic derivatives

- Mathematics
- Proceedings of the Royal Society A
- 2020

The Euler–Maclaurin (EM) formulae relate sums and integrals. Discovered nearly 300 years ago, they have lost none of their importance over the years, and are nowadays routinely taught in scientific… Expand

Plain correlation asymptotes to predict the center and mean temperatures and total heat transfer in simple solid objects with uniform surface temperature at limiting small-time conditions

- Materials Science
- International Journal of Heat and Mass Transfer
- 2019

Abstract Within the platform of unsteady, one-dimensional heat conduction in simple solid objects (large plate, long cylinder and sphere) cooled/heated with uniform surface temperature, the three… Expand

Simple Formulas to Predict Center and Mean Temperatures and Total Heat Transfer in Regular Configurations With Surface Temperature Under Small- and Large-Time Conditions

- Materials Science
- Journal of Thermal Science and Engineering Applications
- 2019

Simple formulas for the prediction of three important thermal quantities, the center temperature, the mean temperature, and the total heat transfer in regular configurations (large plane wall, long… Expand

Morphogenesis of the Zeta Function in the Critical Strip by Computational Approach

- Mathematics
- 2018

This article proposes a morphogenesis interpretation of the zeta function by computational approach by relying on numerical approximation formulae between the terms and the partial sums of the… Expand

Summation Formulas of Euler–Maclaurin and Abel–Plana: Old and New Results and Applications

- Mathematics
- 2017

Summation formulas of the Euler–Maclaurin and Abel–Plana and their connections with several kinds of quadrature rules are studied. Besides the history of these formulas, several of their… Expand

Rationality of the spectral action for Robertson-Walker metrics and the geometry of the determinant line bundle for the noncommutative two torus

- Mathematics
- 2016

In noncommutative geometry, the geometry of a space is given via a spectral triple (A,H, D). Geometric information, in this approach, is encoded in the spectrum of D and to extract them, one should… Expand

Computing Energy Eigenvalues of Anharmonic Oscillators using the Double Exponential Sinc collocation Method

- Physics, Mathematics
- 2014

A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}= -\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where the potential is given by $V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with… Expand

FAMILIES OF EULER-MACLAURIN FORMULAE FOR COMPOSITE GAUSS-LEGENDRE AND LOBATTO QUADRATURES

- 2014

AMS Mathematics Subject Classification (2000): 65D30, 65D32, 40C15

Methods for the computation of slowly convergent series and finite sums based on Gauss-Christoffel quadratures †

- Mathematics
- 2014

In this paper we give an account on summation/integration methods for the computation of slowly convergent series and finite sums. The methods are based on Gauss-Christoffel quadrature rules with… Expand

A Recurrence Relation for Bernoulli Numbers

- Mathematics
- 2013

Inspired by a result of Saalsch¨utz, we prove a recurrence relation forBernoulli numbers. This recurrence relation has an interesting connection with real cyclotomic fields.