Sentence examples for falling function from inspiring English sources

In [1, 2], the authors discussed properties of the generalized falling function, a corresponding power rule for fractional delta-operators and the commutativity of fractional sums.

For example, Atici and Eloe [3] discussed the properties of the generalized falling function, the corresponding power rule for fractional delta operators, and the commutativity of fractional sums.

For example, Atici and Eloe discussed the properties of the generalized falling function, a corresponding power rule for fractional delta-operators, and the commutativity of fractional sums in [1].

Definition 2.1 We define the generalized falling function by t α ̲ : = Γ ( t + 1 ) Γ ( t + 1 − α ), for any t and α, for which the right-hand side is defined.

We define the generalized falling function by (t^{underline{alpha}}:=frac{Gamma (t+1)}{Gamma(t+1-alpha)}), for any t and α for which the right-hand side is defined.

It is well known that the falling function is defined by (t^{underline{nu}}=frac{Gamma(t+1)}{Gamma(t+1-nu)}) for all (t,nuinmathbb{R}) whenever the right-hand side is defined ([31]).

In this section, we give several combinatorics identities involving q-poly-tangent numbers and polynomials in terms of Stirling numbers, falling factorial functions, raising factorial functions, Beta functions, Bernoulli polynomials of higher order, and Frobenius-Euler functions of higher order.

In this paper, we investigated the effects of a 16-week fall-prevention intervention on strength, balance, fear of falling, and function, with a cluster, randomized approach, in the GP office setting.

For any t and ν, the falling factorial function is defined as t ν ̲ = Γ ( t + 1 ) Γ ( t + 1 − ν ).

For any t and ν, the falling factorial function is defined as t^{underline{nu}} =frac{Gamma(t+1)}{Gamma(t+1-nu }, provided t+1-nu } right-hand side is well defined.

From the definition of falling factorial function (t^{(cdot)}), we deduce that (t^{ -alpha)}) is non-increasing for any (alphageq0), (t^{ -alphat is, (t^{(-alpha)}leq(t-beta)^{(-alpha)}) for (alpha geq0), (betageq0) and (t>beta-1).