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The Euler numbers and their last digits

Published online by Cambridge University Press:  20 June 2025

Warren P. Johnson
Warren P. Johnson*
Affiliation:
Connecticut College, 270 Mohegan Avenue, New London, CT 06320 USA e-mail: wpjoh@conncoll.edu

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The Euler numbers are the coefficients En in the expansion

(1)

Since sec x is an even function and tan x an odd one, this decouples into

(2)

and

(3)

where all three series converge if and E2n + 1 are sometimes called the secant numbers (or secant coefficients) and tangent numbers (or tangent coefficients) respectively.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 575 , July 2025, pp. 259 - 264
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Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

References

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