Application of Basic Hypergeometric Series to Stable Analytic Continuation
نویسنده
چکیده
Stable sampling formula using basic hypergeometric series for reconstructing analytic functions from exponentially spaced samples is considered. Criterion for selecting regularizing parameter and error estimates are obtained.
منابع مشابه
Curious Extensions of Ramanujan’s 1ψ1 Summation Formula
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan’s 1ψ1 summation and a very-well-poised 4ψ6 summation as special c...
متن کاملAnalytic Continuation of the Generalized Hypergeometric Series near Unit Argument with Emphasis on the Zero-balanced Series
Various methods to obtain the analytic continuation near z = 1 of the hypergeometric series p+1Fp(z) are reviewed together with some of the results. One approach is to establish a recurrence relation with respect to p and then, after its repeated use, to resort to the well-known properties of the Gaussian hypergeometric series. Another approach is based on the properties of the underlying gener...
متن کاملCurious Extensions of Ramanujan ’ s
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeomet-ric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan's 1 ψ 1 summation and a very-well-poised 4 ψ 6 summation as spec...
متن کاملA Multidimensional Generalization of Shukla's 8 Ψ 8 Summation
Abstract. We give an r-dimensional generalization of H. S. Shukla’s very-wellpoised 8ψ8 summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system Ar−1, or equivalently, the unitary group U(r). Our proof, which is already new in the one-dimensional case, utilizes an Ar−1 nonterminating very-well-poised 6φ5 summation by S. C. Milne, a ...
متن کاملSome decomposition formulas of generalized hypergeometric functions and formulas of an analytic continuation of the Clausen function
In this paper, using similar symbolical method of Burchnall and Chaundy formulas of expansion for the generalized hypergeometric function were constructed. By means of the found formulas of expansion the formulas of an analytic continuation for hypergeometric function of Clausen is defined. The obtained formulas of an analytic continuation express known hypergeometric Appell function F2 (a; b1,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005