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2 giorni fa · Bernoulli's formula is sometimes called Faulhaber's formula after Johann Faulhaber who also found remarkable ways to calculate sums of powers. Faulhaber's formula was generalized by V. Guo and J. Zeng to a q-analog. Taylor series. The Bernoulli numbers appear in the Taylor series expansion of many trigonometric functions and hyperbolic functions.
1 giorno fa · Lagrangian mechanics describes a mechanical system as a pair (M, L) consisting of a configuration space M and a smooth function within that space called a Lagrangian. For many systems, L = T − V, where T and V are the kinetic and potential energy of the system, respectively. [3]
2 giorni fa · e. Newton's laws of motion are three laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a ...
3 giorni fa · Das Buch besteht aus dem letzten von drei Bänden der Ausgabe der Korrespondenz zwischen den Mathematikern Johann I. Bernoulli (1667-1748) und Pierre Varignon (1654-1722).Es enthält die 95 Briefe, die von 1714 bis 1722, dem Todesjahr von Varignon, ausgetauscht wurden. Mit der Veröffentlichung der vollständig kommentierten kritischen Ausgabe ...
3 giorni fa · Im Schriftwechsel zwischen Leibniz und Johann I Bernoulli wird der Funktionsbegriff von der Geometrie losgelöst und in die Algebra übertragen. In Beiträgen von 1706, 1708 und 1718 stellt Bernoulli diese Entwicklung dar. 1748 präzisiert Leonhard Euler , ein Schüler Johann Bernoullis, in seinem Buch Introductio in analysin infinitorum den Funktionsbegriff weiter.
4 giorni fa · A Bessel equation is a special case of a confluent hypergeometric equation. The Bessel function of the first kind of order ν: where Γ(z) = ∫∞0xz − 1e − xdx is the gamma function. There are two Bessel functions of the second kind of order ν: one is called the Weber function: Yν(x) = cosνπJν(x) − J − ν(x) sinνπ.
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