negative integers
Estimating the polygamma functions for negative integers
... Ozcag et al. [, ] applied the neutrix limit to extend the definition of incomplete beta function and its partial derivatives for negative integers. Also, the digamma function was generalized for ...
8
Ascent sequences and upper triangular matrices containing non-negative integers
... For sequences x and y of non-negative integers, let x ⊕ y = xy ′ , where y ′ is obtained from y by adding 1 + max(x) to each of its letters, and juxtaposition denotes concatenation. For example (3 , 2 , 0 , ...
16
A new proof of Smory´nski’s theorem
... non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the ...
8
Some Higher Order Triangular Sum Labeling of Graphs
... A p,q graph G is said to admit n order triangular sum labeling if its vertices can be labeled by non negative integers such that the induced edge labels obtained by the sum of the labels[r] ...
8
Tetrahedral and Pentatopic Sum Labeling of Graphs
... non negative integers such that the induced edge labels obtained by the sum of the labels of end vertices are the first q tetrahedral or pentatope ...
5
Three Fascinating Pairs
... Number theory along with Geometry [1] is one of the two oldest branches of Mathematics. Number theory, as a fundamental body of knowledge, has played a significant role in the development of Mathematics. The study of ...
9
Some Polygonal Sum Labeling of Paths
... A (p,q) graph G is said to admit a polygonal sum labeling if its vertices can be labeled by non -negative integers such that the induced edge labels obtained by the sum of the labels of end vertices are the ...
5
Pentagonal Graceful Labeling of Caterpillar Graphs
... non negative integers such that the induced edge labels obtained by the absolute difference of the labels of end vertices are the first 𝒒 pentagonal ...
5
Vol 9, No 4 (2018)
... Definition 1.5: A graph is said to be arithmeticif its vertices can be assigned distinct non negative integers in such a way that the value of the edges are obtained as sum of the valu[r] ...
9
Vol 1, No 3 (2010)
... Since Pochhammer's symbol is associated with Gamma function and Gamma function is undefined for zero and negative integers therefore numerator and denominator parameters are adjusted in[r] ...
10
q Riemann zeta function
... In a recent paper, the q -analogue of Riemann zeta function was studied by Cherednik (see [1]). In [1], we can consider the q -Bernoulli numbers which can be viewed as an interpolation of the q -analogue of Riemann zeta ...
7
The stieltjes transform of distributions
... compact set of the complex plane not meeting the negative real axis, then for fixed non-negative integers m and k, there exists a constant B.. of the complex plane not meeting.[r] ...
18
Vol 9, No 4 (2018)
... Gaussian integers, denoted Z[i], are the complex numbers of the form a+bi, where a, b ϵ Z and i 2 = ...Gaussian integers is one of ±1, ± ...Gaussian integers α and β are relatively prime if their ...
6
On the Weil étale Cohomology of S Integers
... In this thesis, we first briefly introduce the history of the Weil-´ etale cohomology theory of arithmetic schemes and review some important results established by Lichtenbaum, Flach and Morin. Next we generalize the ...
75
Finding the ring of integers and its algorithms in algebraic number theory
... of integers of a given algebraic number ...of integers, one finds a subring of the number field that one may view as the "best guess" one has for the ring of ...
5
SRC RR 145 pdf
... specialization specification IntSetSSpec f state field elements; // A mathematical set of integers state field cache; // Also a mathematical set of integers invariant cache ⊆ elements //[r] ...
108
ECM at Work
... Today, more than 25 years after its invention by Hendrik Lenstra Jr., the elliptic curve method [24] (ECM) remains the asymptotically fastest integer factorization method for finding relatively small prime factors of ...
17
Partitioning the positive integers with higher order recurrences
... some choice positive integer for which 2.1 holds for For a given Stolarsky array, if k is the least determined, and identity 0, then these integers are uniquely of integers ck-, c_2,...,[r] ...
6
Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field
... Euler then continues his proof by treating the factors (y + √ −2) and (y − √ −2) as if they were relatively prime rational integers and then makes arguments which would normally hold in the ring Z . Euler exploits ...
38
Fast multiplication of multiple-precision integers
... functions to the simplified multiplication 3.3.3 modular modular multiplication particular already very decrease bits using num the ordinary according to the formula for the bit complexi[r] ...
95