On q-summation and confluence
نویسندگان
چکیده
This paper is divided in two parts. In the first part we consider a convergent q-analog of the divergent Euler series, with q ∈ (0, 1), and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding q-difference equation. In the second part, we work under the assumption q ∈ (1,+∞). In this case, at least four different q-Borel sums of a divergent power series solution of an irregular singular analytic q-difference equations are spread in the literature: under convenient assumptions we clarify the relations among them.
منابع مشابه
0 Summation Formulas for the product of the q - Kummer Functions from E q ( 2 )
Using the representation of Eq(2) on the non-commutative space zz ∗−qz∗z = σ; q < 1, σ > 0 summation formulas for the product of two, three and four q-Kummer functions are derived.
متن کاملOn a more accurate multiple Hilbert-type inequality
By using Euler-Maclaurin's summation formula and the way of real analysis, a more accurate multipleHilbert-type inequality and the equivalent form are given. We also prove that the same constantfactor in the equivalent inequalities is the best possible.
متن کاملImpact of the Confluence Angle on Flow Field and Flowmeter Accuracy in Open Channel Junctions
Open channel junction is one of the most common hydraulic structures that are used in various practical situations such as sewer, drainage, and flood control systems. Knowing the fluid flow behavior, is one of the most important topics in designing the efficient open channel junctions. The complexity and deviation of flow in the junction’s zone disrupts the proper functioning of the flowmeter d...
متن کاملOn an Extension of Extended Beta and Hypergeometric Functions
Abstract. Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically investigate several properties of each of these extended functions, such as their various integral representations, Mellin transforms, derivatives, tran...
متن کاملConfluence Results for a Quantum Lambda Calculus with Measurements
A strong confluence result for Q, a quantum λ-calculus with measurements, is proved. More precisely, confluence is shown to hold both for finite and infinite computations. The technique used in the confluence proof is syntactical but innovative. This makes Q different from similar quantum lambda calculi, which are either measurement-free or provided with a reduction strategy.
متن کامل