Human Proofs of Identities by Osburn and Schneider
نویسنده
چکیده
Osburn and Schneider recently derived several combinatorial identities involving harmonic numbers using the computer programm Sigma. Here, they are derived by partial fraction decomposition and creative telescoping.
منابع مشابه
Automated Proofs for Some Stirling Number Identities
We present computer-generated proofs of some summation identities for (q-)Stirling and (q-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number identities with a recurrence solver for difference fields.
متن کاملGaussian Hypergeometric series and supercongruences
Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number of Fp points on algebraic varieties and to Fourier coefficients of modular forms. In this paper, we explicitly determine these functions modulo higher powers of p and discuss an application to super...
متن کاملRogers-ramanujan Type Identities for Alternating Knots
We highlight the role of q-series techniques in proving identities arising from knot theory. In particular, we prove Rogers-Ramanujan type identities for alternating knots as conjectured by Garoufalidis, Lê and Zagier.
متن کاملComputer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them.
متن کاملUTAH STATE CONFERENCE Determinantal Identities Revisited
This article reports on a talk given by the second-named author which is based on the partly expository paper [1]. The paper contains statements and proofs of determinantal identities ascribed to the mathematicians whose names occur in the title of [1], including the "laws" of Muir and Cayley. This account is followed by a formal treatment of determinantal identities which permits us to state t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007