Some operator identities and q-series transformation formulas

نویسندگان

چکیده

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

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

A Symbolic Operator Approach to Power Series Transformation-Expansion Formulas

Here expounded is a kind of symbolic operator method by making use of the defined Sheffer-type polynomial sequences and their generalization, which can be used to construct many power series transformation and expansion formulas. The convergence of the expansions are also discussed. AMS Subject Classification: 41A58, 41A80, 65B10, 05A15, 33C45, 39A70.

متن کامل

q–ENGEL SERIES EXPANSIONS AND SLATER’S IDENTITIES

We describe the q–Engel series expansion for Laurent series discovered by John Knopfmacher and use this algorithm to shed new light on partition identities related to two entries from Slater’s list. In our study Al-Salam/Ismail and Santos polynomials play a crucial rôle. Dedicated to the memory of John Knopfmacher 1937–1999

متن کامل

Supernomial coefficients, polynomial identities and q-series

q-Analogues of the coefficients of x in the expansion of ∏N j=1(1 + x + · · · + x )j are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the “q-supernomial coefficients” are derived, and a combinatorial interpretation using generalized Durfee dissection partitions is given. Polynomial identities of boson–fermion-type, based on the continued fraction...

متن کامل

TWO IDENTITIES FOR MULTIPLE HARMONIC q-SERIES

Abstract. We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial coefficients. Special cases of these identities—for example, with all parameters equal to 1—have occurred in the literature. The special case with only ...

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

ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2003

ISSN: 0012-365X

DOI: 10.1016/s0012-365x(02)00626-x