An Identity of Andrews, Multiple Integrals, and Very-well-poised Hypergeometric Series
نویسنده
چکیده
Abstract. We give a new proof of a theorem of Zudilin that equates a very-well-poised hypergeometric series and a particular multiple integral. This integral generalizes integrals of Vasilenko and Vasilyev which were proposed as tools in the study of the arithmetic behaviour of values of the Riemann zeta function at integers. Our proof is based on limiting cases of a basic hypergeometric identity of Andrews.
منابع مشابه
A Bailey Tree for Integrals
Series and integrals of hypergeometric type have many applications in mathematical physics. Investigation of the corresponding special functions can therefore be relevant for various computations in theoretical models of reality. Bailey chains provide powerful tools for generating infinite sequences of summation or transformation formulas for hypergeometric type series. For a review of the corr...
متن کاملA NONTERMINATING 8φ7 SUMMATION FOR THE ROOT System Cr
where aq = bcdef (cf. [9, Eq. (2.11.7)]), is one of the deepest results in the classical theory of basic hypergeometric series. It contains many important identities as special cases (such as the nonterminating 3φ2 summation, the terminating 8φ7 summation, and all their specializations including the q-binomial theorem). One way to derive (1.1) is to start with a particular rational function ide...
متن کاملOverpartition Pairs
An overpartition pair is a combinatorial object associated with the q-Gauss identity and the 1ψ1 summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of q-difference equations for well-poised basic hypergeometric series and the theory of Bailey chains.
متن کاملWell-poised Hypergeometric Service for Diophantine Problems of Zeta Values
It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studing arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in 1 and ζ(4) = π/90 yielding a conditional upper bound for the irrationality measure of ζ(4); (2) a second-order Apéry-like recursion...
متن کاملTHE At AND Q BAILEY TRANSFORM AND LEMMA
We announce a higher-dimensional generalization of the Bailey Transform, Bailey Lemma, and iterative "Bailey chain" concept in the setting of basic hypergeometric series very well-poised on unitary Ae or symplectic Q groups. The classical case, corresponding to A¡ or equivalently U(2), contains an immense amount of the theory and application of one-variable basic hypergeometric series, includin...
متن کامل