Pafnuty Chebyshev

Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв) (1821-1894) was a Russian mathematician. His name is also transliterated as Tchebycheff or Tschebyscheff.

The Chebyshev polynomials are named in his honor.

In analog electronics there exists a filter family named "Chebyshev filters".

He is also known for his work in the field of probability and statistics. Chebyshev's inequality says that the probability that a random variable is more than a standard deviations away from its mean is no more than 1/a². If μ is the mean (or expected value) and σ is the standard deviation, then we can state the relation as:

<math>P(\left|X-\mu\right|>a\sigma)\leq\frac{1}{a^2}</math>

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

See also:

• Chebotarev's density theorem[?] - (algebraic number theory)
• Bienaymé-Chebyshev inequality - (1853|1866)

<math>P(\left|\xi-E\xi\right|>a)\leq\frac{\mbox{var}\,\xi}{a^2}</math>