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Encyclopedia > Chebyshev
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Pafnuty Lvovich Chebyshev

Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв) (May 4, 1821 - November 26, 1894) was a Russian mathematician. His name is also transliterated as Chebyshov, Tchebycheff or Tschebyscheff (obsolete German transcription).


He was a student of Nikolai Brashman. His own most illustrious student was Andrei Markov.


He is known for his work in the field of probability and statistics. Chebyshev's inequality says that the probability that the outcome of a random variable is more than a standard deviations away from its mean is no more than 1/a2:

Chebyshev's inequality is used to prove the weak law of large numbers and the Bertrand-Chebyshev theorem (1845|1850).


The Chebyshev polynomials are named in his honor.


In electronics and signal processing, the family of electronic filters known as "Chebyshev filters" are named after him.


See also

External link

  • MacTutor biography (http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Chebyshev.html)





  Results from FactBites:
 
Chebyshev biography (3026 words)
Chebyshev always acknowledged the great influence Brashman had been on him while studying at university, and credited him as the main influence in directing his research interests, referring to their "precious personal talks".
Chebyshev continued to aim at international recognition with his second paper, written again in French, appearing in 1844 published by Crelle in his journal.
In the summer of 1846 Chebyshev was examined on his Master's thesis and in the same year published a paper based on that thesis, again in Crelle's journal.
Chebyshev Filters (116 words)
Chebyshev filters are used to separate one band of frequencies from another.
The primary attribute of Chebyshev filters is their speed, typically more than an order of magnitude faster than the windowed-sinc.
This chapter presents the information needed to use Chebyshev filters without wading through a mire of advanced mathematics.
  More results at FactBites »


 

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