Automatic Proofs of Identities

نویسندگان

  • Bruno Salvy
  • Flavia Stan
چکیده

We present the ideas behind algorithmic proofs of identities involving sums and integrals of large classes of special functions. Recent results allowed a new extension of the class of holonomic functions.

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

Automatic Proofs and Counterexamples for Some Ortholattice Identities

This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill.

متن کامل

FINE-TUNING ZEILBERGER’S ALGORITHM The Methods of Automatic Filtering and Creative Substituting

It is shown how the performance of Zeilberger’s algorithm and its q-version for proving (q-)hypergeometric summation identities can be dramatically improved by a frequently missed optimization on the programming level and by applying certain kinds of substitutions to the summand. These methods lead to computer proofs of identities for which all existing programs have failed so far.

متن کامل

Combinatorial Proofs of q-Series Identities

We provide combinatorial proofs of six of the ten q-series identities listed in [3, Theorem 3]. Andrews, Jiménez-Urroz and Ono prove these identities using formal manipulation of identities arising in the theory of basic hypergeometric series. Our proofs are purely combinatorial, based on interpreting both sides of the identities as generating functions for certain partitions. One of these iden...

متن کامل

Hybrid Proofs of the q-Binomial Theorem and Other Identities

We give “hybrid” proofs of the q-binomial theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities d...

متن کامل

Combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians

The classic Cayley identity states that det(∂) (detX) = s(s+ 1) · · · (s+ n− 1) (detX) where X = (xij) is an n× n matrix of indeterminates and ∂ = (∂/∂xij) is the corresponding matrix of partial derivatives. In this paper we present straightforward combinatorial proofs of a variety of Cayley-type identities, both old and new. The most powerful of these proofs employ Grassmann algebra (= exterio...

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 2011