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Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals. Some expressions which are (amazingly) related to pi have been evaluated. In addition, a continual battle has been waged just to break the records computing digits of this number; records have been set using rapidly converging series, ultra fast algorithms and really surprising ones, calculating isolated digits. The development of powerful computers has played a fundamental role in these achievements of calculus.
This paper is an exposition and review of the research related to the Riemann Hypothesis starting from the work of Riemann and ending with a description of the work of G. Spencer-Brown.
This is a collection of definitions, notations and proofs for the Bernoulli numbers $B_n$ appearing in formulas for the sum of integer powers, some of which can be found scattered in the large related historical literature in French, English and Germ
In this paper will be proved the existence of a formula to reduce a tetration of base $2^{k}$ and $5^{k}$ $mod 10^{n}$. Indeed, last digits of a tetration are the same starting from a certain hyper-exponent; In order to compute the last digits of tho
This is an English translation of the Latin original De summa seriei ex numeris primis formatae ${1/3}-{1/5}+{1/7}+{1/11}-{1/13}-{1/17}+{1/19}+{1/23}-{1/29}+{1/31}-$ etc. ubi numeri primi formae $4n-1$ habent signum positivum formae autem $4n+1$ sign
Appearing in 1921 as an equation for small-amplitude waves on the surface of an infinitely deep liquid, the Nekrasov equation quickly became a source of new results. This manifested itself both in the field of mathematics (theory of nonlinear integra