Euler–Boole summation
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Euler–Boole summation is a method for summing 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.
References[edit]
- 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, JSTOR 40391116
- Nico M. Temme: Special Functions: An Introduction to the Classical Functions of Mathematical Physics, Wiley, 2011, ISBN 9781118030813, pp. 17–18