Some q-Dixon-like summation formulas

نویسندگان

  • Victor J. W. Guo
  • Ya-Zhen Wang
چکیده

We give a q-analogue of some Dixon-like summation formulas obtained by Gould and Quaintance [Fibonacci Quart. 48 (2010), 56–61] and Chu [Integral Transforms Spec. Funct. 23 (2012), 251–261], respectively. For example, we prove that

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New Proofs of Some q-Summation and q-Transformation Formulas

We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.

متن کامل

Evaluations of series of the $q$-Watson, $q$-Dixon, and $q$-Whipple type

Evaluations of series of the q-Watson, q-Dixon, and q-Whipple type Chuanan Wei1∗ Xiaoxia Wang2† 1 Department of Medical Informatics, Hainan Medical University, China 2 Department of Mathematics, Shanghai University, China received 16th Apr. 2016, revised 1st May 2017, accepted 6th June 2017. Using q-series identities and series rearrangement, we establish several extensions of q-Watson formulas...

متن کامل

Transformations of Ramanujan’s Summation Formula and Its Applications

In this paper, we obtain some new transformation formulas for Ramanujan’s 1ψ1 summation formula and also establish some eta-function identities. We also deduce a q-Gamma function identity, a q-integral and some interesting series representations for π 3/2 2 √ 2Γ2(3/4) and the beta function B(x,y).

متن کامل

Contiguous Extensions of Dixon ’ s Theorem on the Sum of a 3 F 2

In 1994, Lavoie et al. have succeeded in artificially constructing a formula consisting of twenty three interesting results, except for five cases, closely related to the classical Dixon’s theorem on the sum of a 3F2 by making a systematic use of some known relations among contiguous functions. We aim at presenting summation formulas for those five exceptional cases that can be derived by using...

متن کامل

0 Summation Formulas for the product of the q - Kummer Functions from E q ( 2 )

Using the representation of Eq(2) on the non-commutative space zz ∗−qz∗z = σ; q < 1, σ > 0 summation formulas for the product of two, three and four q-Kummer functions are derived.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014