multiplication theorem sentence in Hindi
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- One may construct a function obeying the multiplication theorem from any totally multiplicative function.
- Gauss also arrived at the notion of reciprocal ( inverse ) determinants, and came very near the multiplication theorem.
- Gauss also proved the multiplication theorem of the gamma function and investigated the connection between the gamma function and elliptic integrals.
- The following tabulates the various appearances of the multiplication theorem for finite characteristic; the characteristic zero relations are given further down.
- The multiplication theorem for the Bernoulli polynomials then follows as a special case of the multiplicative function f ( n ) = n ^ {-s }.
- Two series may be multiplied ( sometimes called the " multiplication theorem " ) : For any two arithmetic functions f and g, let h = f * g be their Dirichlet convolution.
- The Bernoulli polynomials may be obtained as a limiting case of the periodic zeta function, taking " s " to be an integer, and thus the multiplication theorem there can be derived from the above.
- The next contributor of importance is Binet ( 1811, 1812 ), who formally stated the theorem relating to the product of two matrices of " m " columns and " n " rows, which for the special case of reduces to the multiplication theorem.
- On the same day ( November 30, 1812 ) that Binet presented his paper to the Academy, Cauchy also presented one on the subject . ( See Cauchy Binet formula . ) In this he used the word " "'determinant " "'in its present sense, summarized and simplified what was then known on the subject, improved the notation, and gave the multiplication theorem with a proof more satisfactory than Binet's.
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