منابع مشابه
Asymptotic Expansions of Certain Partial Theta Functions
We establish an asymptotic expansion for a class of partial theta functions generalizing a result found in Ramanujan’s second notebook. Properties of the coefficients in this more general asymptotic expansion are studied, with connections made to combinatorics and a certain Dirichlet series.
متن کاملHardy-petrovitch-hutchinson’s Problem and Partial Theta Function
In 1907, M. Petrovitch [20] initiated the study of a class of entire functions all whose finite sections (i.e. truncations) are real-rooted polynomials. He was motivated by previous studies [17] of E. Laguerre on uniform limits of sequences of real-rooted polynomials and by an interesting result of G. H. Hardy [10]. An explicit description of this class in terms of the coefficients of a series ...
متن کاملMinimal partial realization from generalized orthonormal basis function expansions
A solution is presented for the problem of realizing a discrete-time LTI state-space model of minimal McMillan degree such that its :rst N expansion coe;cients in terms of generalized orthonormal basis match a given sequence. The basis considered, also known as the Hambo basis, can be viewed as a generalization of the more familiar Laguerre and two-parameter Kautz constructions, allowing genera...
متن کاملData Leaves with Partial Expansions
We present an exact performance analysis, under random insertions, of file organizations that use multi-bucket data leaves and perform partial expansions before splitting. We evaluate the expected disk space utilization of the file, and show how the expected search and insert costs can be estimated. The analytical results are confirmed by simulations. The analysis can be used to investigate bot...
متن کاملOn the Difference of Partial Theta Functions
n≥0(−1) nq (n−1)n 2 xn are called partial theta functions. In his lost noteboook, Ramanujan recorded many identities for these functions. A few years ago Warnaar found an elegant formula for a sum of two partial theta series. Subsequently, Andrews and Warnaar established a similar result for the product of two partial theta functions. In this note we discuss the relation between the Andrews–War...
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: Tohoku Mathematical Journal
سال: 1990
ISSN: 0040-8735
DOI: 10.2748/tmj/1178227699