Jacques G'elinas

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20112020

most citedOriginal proofs of Stirling's series for log(n!)

2 citations · 3 across the 5 of their papers we have counts for

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math.HO2020

Blissard's trigonometric series with closed-form sums

Jacques Gélinas

This is a summary and verification of an elementary note written by John Blissard in 1862 for the Messenger of Mathematics. A general method of discovering trigonometric series hav…

math.HO2019

Definitions, notations and proofs for Bernoulli numbers

Jacques Gélinas

This is a collection of definitions, notations and proofs for the Bernoulli numbers $B_{n}$ appearing in formulas for the sum of integer powers, some of which can be found scattered…

math.HO2017★ 2 cited

Original proofs of Stirling's series for log(n!)

Jacques Gélinas

Transcription into modern notations of the derivation by Stirling and De Moivre of an asymptotic series for $lo g (n!)$ , usually called Stirling's series. The previous discovery by…

math.HO2011

An easy method for finding the integral of the formula $\int (x^{n + p} - 2 x^{n} cos ζ + x^{n - p}) / (x^{2 n} - 2 x^{n} cos θ + 1) d x / x$ when the upper limit of integration is $x = 1$ or $x = \infty$

Leonhard Euler, Jacques Gélinas

This is a translation of an article presented by Leonhard Euler on 18 March 1776 (Opera Omnia I-XVIII, pp. 265-290) and of summaries for it by Siméon Denis Poisson in 1820 and by H…

Blissard's trigonometric series with closed-form sums

Definitions, notations and proofs for Bernoulli numbers

Original proofs of Stirling's series for log(n!)

An easy method for finding the integral of the formula ∫(xn+p−2xncosζ+xn−p)/(x2n−2xncosθ+1)dx/x when the upper limit of integration is x=1 or x=∞

An easy method for finding the integral of the formula $\int (x^{n + p} - 2 x^{n} cos ζ + x^{n - p}) / (x^{2 n} - 2 x^{n} cos θ + 1) d x / x$ when the upper limit of integration is $x = 1$ or $x = \infty$