Euler–Boole summation

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Euler–Boole summation is a summation method for alternating series based on Euler's polynomials, which are defined by

The concept is named after Leonhard Euler and George Boole.

The periodic Euler functions are

The Euler–Boole formula to sum alternating series is

where , , and is the kth derivative.


  • Jonathan M. Borwein, Neil J. Calkin, Dante Manna: Euler-Boole Summation Revisited. The American Mathematical Monthly, Vol. 116, No. 5 (May, 2009), pp. 387–412 (online,JSTOR)
  • Nico M. Temme: Special Functions: An Introduction to the Classical Functions of Mathematical Physics. Wiley, 2011, ISBN 9781118030813, pp. 17–18