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Evolution of the Euler-Maclaurin sum formula

Published online by Cambridge University Press:  12 October 2022

Amrik Singh Nimbran
Amrik Singh Nimbran*
Affiliation:
B3-304, Palm Grove Heights, Ardee City, Sector 52, Gurugram, 122003 Haryana, India e-mail: amrikn622@gmail.com
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Extract

The correspondence between the discrete and the continuous is a fascinating theme in mathematics. The Euler-Maclaurin sum formula, discovered independently and almost contemporaneously by Leonhard Euler (1707–1783) and Colin Maclaurin (1698–1746), in the early 1730s, relates the sum of the values of a function at the integers in the interval [a, b] with its integral over [a, b]. It thus equates a discrete sum with a continuous sum (integral) of a related function.

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 443 - 457
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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