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Number of Results: 7 Search : binomial

binomial donâmin Fr.: 1) binôme; 2) binomial 1a) An algebraic expression containing 2 terms, as polynomial
with 2 terms. 1b) Biology: A pair of Latin (or latinized) words
forming a scientific name for organisms. The first word represents the genus, and the second
the species. 2) Of, pertaining to, or consisting of a binomial. From L.L. |

binomial coefficient hamgar-e donâmin Fr.: coefficient binomial
The factor multiplying the variable in a term of a
→ → |

binomial differential degarsâne-ye donâmin Fr.: binôme différentiel An expression of the form
a + bx)^{n},
where ^{p}dxm, n, p, a, and b are constants.→ |

binomial distribution vâbâžeš-e donâmin Fr.: distribution binomiale A probability distribution for independent events for which there are only two possible
outcomes i.e., success and failure.
The probability of p is the probability of success and q = 1 - p the probability of
failure on each trial.
These probabilities are given in terms of the → binomial theorem
expansion of (p + q).^{n}→ |

binomial expansion sopâneš-e donâmin Fr.: expansion binomiale A rule for the expansion of an expression of the form x and y can be any → real numbers
and n is an → integer. The
general formula is known as the → binomial theorem. |

binomial nomenclature nâmgozâri-ye donâmin Fr.: nomenclature binomiale A system introduced by Carl von Linné (1707-1778), the Swedish botanist, in which
each organism is identified by two names. The first is the name of
the genus (generic name), written with a capital letter. The
second is the name of the species (specific name). The generic and specific names are
in Latin and are printed in italic type. For example, human beings belong to species
→ |

binomial theorem farbin-e donâmin Fr.: théorème du binôme A rule for writing an equivalent expansion of an expression such as
( binomial expansion.
The general expression is
(a + b) = &Sigma (^{n}n,k)a,
where the summation is from ^{k}b^{n - k}k = 0 to n, and
(n,k) = n!/[r!(n - k)!].
For n = 2, (a + b).
Historically, the binomial theorem as applied to (^{2} = a^{2} + 2ab + b^{2}a + b)
was known to Euclid (320 B.C.) and other early Greek mathematicians. In the tenth century
the Iranian mathematician Karaji (953-1029) knew the binomial theorem and its accompanying
table of → ^{2}binomial coefficients,
now known as → Pascal's triangle. Subsequently
Omar Khayyam (1048-1131) asserted that he could find the
4th, 5th, 6th, and higher roots of numbers by a special law which did
not depend on geometric figures. Khayyam's treatise concerned with his findings is
lost. In China there appeared in 1303 a work containing the binomial coefficients
arranged in triangular form.
The complete generalization of the
binomial theorem for all values of n, including negative integers,
was established by Isaac Newton (1642-1727). |