Sentence examples for rising function from inspiring English sources

Definition 1 (Rising function).

For t, α ∈ R, the rising function is defined by t α ¯ : = Γ ( t + α ) Γ ( t ).

The (generalized) rising function is defined by t^{overline{r}}:=frac{Gamma(t+r)}{Gamma(t)} for those values of t and r so that the right-hand side of this equation is sensible.

(1)   (ii) For any real number the α rising function becomes t^{overline{alpha}}=frac{Gamma(t+alpha)}{Gamma(t)}, quadmbox{such that } t in mathbb{R}setminus{ldots,-2,-1,0}, 0^{alpha}ne {alpha}=00.

For any real number the α rising function becomes t^{overline{alpha}}=frac{Gamma(t+alpha)}{Gamma(t)}, quadmbox{such that } t in mathbb{R}setminus{ldots,-2,-1,0}, 0^{alpha}ne {alpha}=00.

The term ( t − ρ ( s ) ) α − 1 ¯ in the above definition is the so-called generalized rising function defined by t α ¯ : = Γ ( t + α ) Γ ( t ). for any t, α ∈ R for which the right-hand side is well defined.

We tried fitting the shape to simple math functions (exponentials, polynomials), to solar activity and even to rising functions like world population.

This article is organized as follows: The rest of this section contains definitions and preliminary concepts regarding the rising factorial function, the discrete Mittaf-Leffler functions, Caputo fractional difference and the discrete convolution.

In order to do this, we remind the reader of the rising factorial function.

Regarding the rising factorial function, we observe the following: (i) ∇ ( t α ¯ ) = α t α − 1 ¯.

For any t and ν, the rising factorial function is defined as t ν ¯ = Γ ( t + ν ) Γ ( t ).