Sentence examples for using binomial series expansion from inspiring English sources

Then, each factor of product is fractionalized by taking fractional power and using binomial series expansion.

where binomial series expansion has been applied.

The expressions in (9) and (10) can be obtained by using binomial expansion at first which results the term with power series raised to power ∑ i = 0 ( L B - 1 ) 1 i ! ( γ B γ ̄ B ) i m.

As the intermediate G. ruber (W) pairs are interchangeable amongst coeval couplets (their transitional form inhibits selective categorization), we generated all possible combinations of the couplets in each archive using binomial expansion (See Methods for details).

Then a new range-recursive algorithm using Taylor series expansion is investigated.

Using Taylor series expansion, the nonaffine part of the system is converted into affine form.

Standard errors of statistics were based on approximations using Taylor series expansion (Lynch [1998]) within ASReml.

We analytically evaluate the error probability by using a series expansion of generalized hypergeometric functions.

Using Taylor series expansion for G i, i = 1, 2, …, n, we have.

Confidence intervals in the observed prevalence were estimated by using binomial approximation.

Comparisons of single proportions to hypothesized null values were evaluated using binomial tests.