Extensions of Bailey's transform and applications
نویسندگان
چکیده
The well-known Bailey’s transform is extended. Using the extended transform, we derive hitherto undiscovered ordinary and q-hypergeometric identities and discuss their particular cases of importance, namely, two new q-sums for Saalschützian 4Φ3, new double series Rogers-Ramanujan-type identities of modulo 81, discrete extension of the q-analogs of two quadratic transformations of 2F1, and two new quadratic-cubic transformations of 3F2.
منابع مشابه
Extension of a quadratic transformation due to Exton
Keywords: Quadratic transformation Hypergeometric function of order two Kummer–type transformations Bailey's transform a b s t r a c t By applying various known summation theorems to a general formula based upon Bailey's transform theorem due to Slater, Exton has obtained numerous new quadratic transformations involving hypergeometric functions of two and of higher order. Some of the results ha...
متن کاملSome new extensions of Hardy`s inequality
In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequalityin two and three dimensions
متن کاملSome extensions of Darbo's theorem and solutions of integral equations of Hammerstein type
In this brief note, using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove an existence result for a quadratic integral equation of Hammerstein type on an unbounded interval in two variables which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the effic...
متن کاملA Petri-net based modeling tool, for analysis and evaluation of computer systems
Petri net is one of the most popular methods in modeling and evaluation of concurrent and event-based systems. Different tools have been created to support modeling and simulation of different extensions of Petri net in different applications. Each tool supports some extensions and some features. In this work a Petri net based modeling and evaluation tool is presented that not only supports dif...
متن کاملEntropy of infinite systems and transformations
The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005