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
TAK, TAK!
just compare and confront :
**Johann Bernoulli** „*Series 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* |