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3 days ago · The Swiss mathematician Jakob Bernoulli (1654–1705) was the first to realize the existence of a single sequence of constants B 0, B 1, B 2,... which provide a uniform formula for all sums of powers.
2 days ago · This distribution was derived by Jacob Bernoulli. He considered the case where p = r/(r + s) where p is the probability of success and r and s are positive integers. Blaise Pascal had earlier considered the case where p = 1/2, tabulating the corresponding binomial coefficients in what is now recognized as Pascal's triangle. [45]
3 days ago · The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
Sep 16, 2024 · Even though it was named after the Swiss physicist and mathematician Leonhard Euler, the “discovery” of the constant e is credited to another Swiss mathematician, Jacob Bernoulli. Jacob Bernoulli encountered the constant 𝑒 in 1683 while studying compound interest.
Sep 11, 2024 · Swiss mathematician Jakob Bernoulli, in a proof published posthumously in 1713, determined that the probability of k such outcomes in n repetitions is equal to the kth term (where k starts with 0) in the expansion of the binomial expression (p + q) n, where q = 1 − p.
Sep 9, 2024 · I compared my new approach to the classical formula, which dates back to the 17th century with Jacob Bernoulli’s exploration of compound interest.
3 days ago · A differential equation. y + p(x)y = g(x)yα, where α is a real number not equal to 0 or 1, is called a Bernoulli differential equation. It is named after Jacob (also known as James or Jacques) Bernoulli (1654--1705) who discussed it in 1695. Jacob Bernoulli was born in Basel, Switzerland.
