Generating Function Identities for $\zeta(2n+2), \zeta(2n+3)$ via the WZ Method
نویسندگان
چکیده
منابع مشابه
Generating Function Identities for ζ(2n+2), ζ(2n+3) via the WZ Method
Using WZ-pairs we present simpler proofs of Koecher, Leshchiner and BaileyBorwein-Bradley’s identities for generating functions of the sequences {ζ(2n+2)}n≥0 and {ζ(2n + 3)}n≥0. By the same method, we give several new representations for these generating functions yielding faster convergent series for values of the Riemann zeta function.
متن کاملFinding Identities with the WZ Method
Extending the work of Wilf and Zeilberger on WZ-pairs, we describe how new terminating hypergeometric series identities can be derived by duality from known identities. A large number of such identities are obtained by a Maple program that applies this method systematically.
متن کاملHypergeometric series acceleration via the WZ method
Based on the WZ method, some series acceleration formulas are given. These formulas allow us to write down an infinite family of parametrized identities from any given identity of WZ type. Further, this family, in the case of the Zeta function, gives rise to many accelerated expressions for ζ(3). AMS Subject Classification: Primary 05A We recall [Z] that a discrete function A(n,k) is called Hyp...
متن کاملA Mthod for Generating the Turbulent Intermittency Function
A detection method based on sensitization of a squared double differentiated signal is developed which discriminates the turbulent zones from laminar zones quite accurately. The procedure adopts a variable threshold and a variable hold time of the order of the Kolmogorov time scale. The output file so generated, includes all the information for further analysis of the turbulent signal.
متن کاملThe Markov-WZ Method
Andrei Markov’s 1890 method for convergence-acceleration of series bears an amazing resemblance to WZ theory, as was recently pointed out by M. Kondratieva and S. Sadov. But Markov did not have Gosper and Zeilberger’s algorithms, and even if he did, he wouldn’t have had a computer to run them on. Nevertheless, his beautiful ad-hoc method, when coupled with WZ theory and Gosper’s algorithm, lead...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/759