Wzór Brooka Taylora to wzór sporo wcześniej odkryty przez Johanna Bernoulliego ?

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czy wiecie że

do you know that

wzór Brooka Taylora to wzór

sporo wcześniej odkryty przez

Johanna Bernoulliego ?
przeczytajcie zatem historyczną notę na początku:

[see historical note in ]

A. Krzysztof Kwasniewski Bernoulli-Taylor formula for psi-umbral difference calculus.

ArXiv: math.GM/0312401 December 2003 published as

[84] A.K.Kwaśniewski On -umbral difference calculus Bernoulli-Taylor formula with a Cauchy-type remainder

Bulletin de la Societe des Sciences et des Lettres de £ódź (54) Serie: Recherches sur les Deformations Vol. 44 (2004) pp. 21-29, ArXiv: math.GM/0312401 December 2003

see more in publikacje in http://ii.uwb.edu.pl/akk/index.html

zaglądnijcie też do:

cytowanego w [01] jako [1] XIX-wiecznego , napisanego w cyrylicy- eseju Akademika Sonina ... esej jest dostępny w Bibliotekach np. na Sosnowej


just compare and confront :

Johann BernoulliSeries universalissima" in Acta Erudicorum (1694) Leipzig

with the book of

Brook Taylor Methodus incrementorum directa et inversa (1715) London;
Confrontation entitles one to call the corresponding expansion formulas

Bernoulli - Taylor formulas or Bernoulli - Taylor series.

Well -

that is not end of the story

it has been just thus started!

read more in parallel articles an/or links in the same folder

ad. History:

Johann Bernoulli (1667-1748) was elected a fellow of the academy of St Petersburg.

 Johann Bernoulli - the Discoverer of Series Universalissima was "Archimedes of his

age" and this is indeed inscribed on his tombstone.

 The Acta Eruditorum was first published in Leipzig in 1682 under the auspices of the Collegium Gellianum, with support from the Duke of Saxony. Its purpose was to provide announcements of and abstracts to notable publications of the time--this included long-standing books and articles as well as contemporary works. ...............

Volume one is a good indicator of its auspicious beginnings; it includes articles by ....., Gottfried Wilhelm Leibniz and Johann Bernoulli. Later contributors (some posthumous) were Pascal, Huygens, Halley, and Descartes.

René Descartes (1596 - 1650)

Blaise Pascal (1623 - 1662)

Gottfried Wilhelm Leibniz (1646 - 1716)

Johann Bernoulli (1667 - 1748)

Nikolay Yakovlevich Sonin (1849 - 1915)

Born: 22 Feb 1849 in Tula, Russia Died: 27 Feb 1915 in Petrograd

attended Moscow University studying mathematics and physics there from 1865 to 1869. He obtained a Master's Degree with a thesis submitted in 1871,

then he taught at the University of Warsaw where he obtained a doctorate in 1874.

He was appointed to a chair in the University of Warsaw in 1876.

In 1894 Sonin moved to St Petersburg where he taught at the University for Women.

Sonin worked on special functions, in particular cylindrical functions. He also worked on the Euler-Maclaurin summation formula.

Other topics Sonin studied included Bernoulli polynomials (Jacob Bernoulli) and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration.

Together with A A Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian.

from Article by: J J O'Connor and E F Robertson

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