Sums of Powers of Integers and Bernoulli Numbers Clarified | Chapter 02 | Theory and Applications of Physical Science Vol. 2
We exposes a very simple method for calculating at the same time the sums of powers of the first integersand the Bernoulli numbers. This is possible thank to integrations of the equationwhich lead to a formula saying that the vector is the transform of the vector by a matrix built from the Pascal triangle and obtainable by a simple algorithm. Very useful relations between the sums, the Bernoulli numbers are deduced, leading straightforwardly to known and new properties of them. The proof of the Faulhaber formulae on powers sums are outlined briefly at the end.
We exposes a very simple method for calculating at the same time the sums of powers of the first integersand the Bernoulli numbers. This is possible thank to integrations of the equationwhich lead to a formula saying that the vector is the transform of the vector by a matrix built from the Pascal triangle and obtainable by a simple algorithm. Very useful relations between the sums, the Bernoulli numbers are deduced, leading straightforwardly to known and new properties of them. The proof of the Faulhaber formulae on powers sums are outlined briefly at the end.
Author(s) Details
Do Tan Si HoChiMinh-city Physical Association, Vietnam and Université libre de Bruxelles and UEM, Belgium.
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