Sentence examples for multiplication theorem for from inspiring English sources

We note that by setting in Theorem 2.3, we get the following multiplication theorem for the twisted -Bernoulli polynomials.

which is a q-analogue of Raabe's multiplication theorem for the classical Bernoulli polynomials (see, e.g., [8]).

Setting b = 1 in Theorem 2.2, we derive the multiplication theorem for the q-Bernoulli polynomials due to Carlitz [4] [ a ] q n − 1 ∑ j = 0 a − 1 q j β n ( x + j a, q a ) = β n ( a x, q ), (2.17).

Letting q → 1 in Theorem 2.2, one can immediately obtain the generalized multiplication theorem for the classical Bernoulli polynomials (see, e.g., [9 11]) a n − 1 ∑ j = 0 a − 1 B n ( b x + b j a ) = b n − 1 ∑ j = 0 b − 1 B n ( a x + a j b ).

A starting point is the Gauss multiplication theorem [16] for the gamma function, which states that begin{aligned} Gamma (mz)=(2pi )^{frac{1-m}{2}}m^{mz-frac{1}{2}} prod _{j=1}^{m} Gamma biggl( z+ frac{j-1}{m} biggr), quad z neq 0,- frac{1}{m},ldots, end{aligned} (m in mathbb{N}).

We compute the degree using three homotopies, the Leray index theorem and the multiplication theorem.

An extended multiplication theorem and new infinite families of column-orthogonal designs are presented using periodic Golay pairs.

According to the multiplication theorem, the window function multiplication in the time domain is equivalent to the window function convolution in the frequency domain.

This theorem is called the "prime number theorem for geodesics", because it is exactly analogous to the usual "prime number theorem" for whole numbers, which estimates the number of primes less than a given size.

Concerning the undefinability theorem for L ω1,ω1).

Using (2), theorem (4) entails the isomorphism theorem for finitary and finitely algebraizable logics.