An Elementary Proof of the Wallis Product Formula for pi

An Elementary Proof of the Wallis Product Formula for pi

by repeated partial integration. The topic is usually reserved for more advanced calculus courses. The purpose of this note is to show that (1) can be derived using only the mathematics taught in elementary school, that is, basic algebra, the Pythagorean theorem, and the formula π · r 2 for the area of a circle of radius r . Viggo Brun gives an account of Wallis’s method in [1] (in Norwegian). ...

An Elementary Proof of the Hook Formula

The hook-length formula is a well known result expressing the number of standard tableaux of shape λ in terms of the lengths of the hooks in the diagram of λ. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing more than the fundamental theorem of algebra. This proof was suggested by a q, t-analog of the hook formula given ...

An Elementary Proof of Euler's Formula for ζ(2m)

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An Elementary Proof of a Generalization of Bernoulli’s Formula

Generalizing Wallis' Formula

The present note generalizes Wallis’ formula, 2  =  . 7 6 . 5 6 . 5 4 . 3 4 . 3 2 . 1 2 , using the EulerMascheroni constant g and the Glaisher-Kinkelin constant A: 2 ln 2 4 = 3 3 2 . 1 2 . 5 4 3 4