Partial sums of hypergeometric series of unit argument
نویسندگان
چکیده
منابع مشابه
Partial Sums of Hypergeometric Series of Unit Argument
The asymptotic behaviour of partial sums of generalized hypergeometric series of unit argument is investigated.
متن کاملDirichlet L-functions, Elliptic Curves, Hypergeometric Functions, and Rational Approximation with Partial Sums of Power Series
We consider the Diophantine approximation of exponential generating functions at rational arguments by their partial sums and by convergents of their (simple) continued fractions. We establish quantitative results showing that these two sets of approximations coincide very seldom. Moreover, we offer many conjectures about the frequency of their coalescence. In particular, we consider exponentia...
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 کاملPartial reciprocal sums of the Mathieu series
It is well known that the Mathieu series has a wide application in mathematics science. In this paper, we use the elementary method and construct some new inequalities to study the computational problem of the partial reciprocal sums related to the Mathieu series and obtain an interesting inequality and a related identity.
متن کاملPartial Sums of Two Quartic q-Series
X iv :0 90 4. 34 53 v1 [ m at h. C A ] 2 2 A pr 2 00 9 Symmetry, Integrability and Geometry: Methods and Applications SIGMA 5 (2009), 050, 19 pages Partial Sums of Two Quartic q-Series Wenchang CHU † and Chenying WANG ‡ † Dipartimento di Matematica, Università degli Studi di Salento, Lecce-Arnesano P. O. Box 193, Lecce 73100, Italy E-mail: [email protected] ‡ College of Mathematics and Phys...
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: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07010-2