D-finite Numbers
نویسندگان
چکیده
D-finite functions and P-recursive sequences are defined in terms of linear differential and recurrence equations with polynomial coefficients. In this paper, we introduce a class of numbers closely related to D-finite functions and P-recursive sequences. It consists of the limits of convergent P-recursive sequences. Typically, this class contains many well-known mathematical constants in addition to the algebraic numbers. Our definition of the class of D-finite numbers depends on two subrings of the field of complex numbers. We investigate how different choices of these two subrings affect the class. Moreover, we show that D-finite numbers over the Gaussian rational field are essentially the same as the regular holonomic constants, namely the values of D-finite functions at non-singular algebraic number arguments. This result makes it easier to recognize certain numbers as belonging to this class.
منابع مشابه
Twin signed total Roman domatic numbers in digraphs
Let $D$ be a finite simple digraph with vertex set $V(D)$ and arcset $A(D)$. A twin signed total Roman dominating function (TSTRDF) on thedigraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfyingthe conditions that (i) $sum_{xin N^-(v)}f(x)ge 1$ and$sum_{xin N^+(v)}f(x)ge 1$ for each $vin V(D)$, where $N^-(v)$(resp. $N^+(v)$) consists of all in-neighbors (resp.out-neighbors) of $v$, and (...
متن کاملOn the Graphs Related to Green Relations of Finite Semigroups
In this paper we develop an analog of the notion of the con- jugacy graph of nite groups for the nite semigroups by considering the Green relations of a nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a nite semigroup S , we first atte...
متن کاملFuzzy Best Simultaneous Approximation of a Finite Numbers of Functions
Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.
متن کاملOn the natural convective heat transfer from a cold horizontal cylinder over an adiabatic surface
A steady two-dimensional laminar free convection heat transfer from a cold horizontal isothermal cylinder located above an adiabatic floor is studied both experimentally and numerically. In the experimental measurements the effects of cylinder distance from horizontal floor to its diameter (L/D) on heat transfer coefficient is studied for Rayleigh numbers of 3×105 and 6×105. Computations are ma...
متن کاملOn Cosets in Segre’s Product of Partial Linear Spaces
Let D be a set, let p be a finite sequence of elements of D, and let i, j be natural numbers. The functor Del(p, i, j) yields a finite sequence of elements of D and is defined by: (Def. 1) Del(p, i, j) = (p↾(i − 1)) a (p⇂j). We now state several propositions: (1) For every set D and for every finite sequence p of elements of D and for all natural numbers i, j holds rngDel(p, i, j) ⊆ rng p. (2) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1611.05901 شماره
صفحات -
تاریخ انتشار 2016