Series acceleration formulae for beta values
نویسندگان
چکیده
We prove generating function identities producing fast convergent series for the sequences β(2n + 1), β(2n + 2) and β(2n+3), where β is Dirichlet's beta function. In particular, we obtain a new accelerated series for Catalan's constant convergent at a geometric rate with ratio 2 −10 , which can be considered as an analog of Amdeberhan-Zeilberger's series for ζ(3).
منابع مشابه
A Class of Series Acceleration Formulae for Catalan’s Constant
Abstract. In this note, we develop transformation formulae and expansions for the log tangent integral, which are then used to derive series acceleration formulae for certain values of Dirichlet L-functions, such as Catalan’s constant. The formulae are characterized by the presence of an infinite series whose general term consists of a linear recurrence damped by the central binomial coefficien...
متن کاملHypergeometric Functions that Generate Series Acceleration Formulae for Values of the Riemann Zeta Function
was first obtained by A. Markov in 1890, but became more widely known after its appearance in connection with Apéry’s proof of the irrationality of ζ(3). We outline here the role that hypergeometric functions play in generating more general series acceleration formulae for values of the Riemann zeta function at the positive integers. At odd positive integers, we have the formulae of Koecher, an...
متن کاملProducing Gravity Acceleration at Sea Surface in Persian Gulf Using Ellipsoidal Splines
In this paper, a method is proposed for producing gravity acceleration at sea surface in the Persian Gulf. This method is based on the Geoid height from satellite altimetry, high resolution Geopotential models, and ellipsoidal splines. First, the definition of the ellipsoidal spline functions is presented in a Hilbert space, which is consisted of infinitely often differentiable functions. In or...
متن کاملEvaluation of the Formulae Based on Red Blood Cell Indices in Differentiating Between Iron Deficiency Anemia and Beta Thalasemia Minor
Background and Aims: Iron deficiency anemia (IDA) and beta thalassemia minor (BTM) are the most common hypochromic microcytic anemias, and it is regarded important to differentiate between them. several formulae can be taken into consideration based on red blood cell (RBC) parameters in order to distinguish between these two disorders. Hence, the present study intended to evaluate the sensitivi...
متن کاملCellular S-value of beta emitter radionuclide’s determined using Geant4 Monte Carlo toolbox, comparison to MIRD S-values
Introduction: Spatial dose distribution around the radionuclides sources is required for optimized treatment planning in radioimmunotherapy. At present, the main source of data for cellular dosimetry is the s-values provided by MIRD. However, the MIRD s-values have been calculated based on analytical formula in which no electrons straggling is taken to account. In this study, we used Geant4-DNA...
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:
- Discrete Mathematics & Theoretical Computer Science
دوره 12 شماره
صفحات -
تاریخ انتشار 2010