… On the elliptic beta function … Spiridonov VP, Warnaar SO, “Inversions of integral
operators and elliptic beta integrals on root systems”, Adv. Math., 207:1 (2006), 91–132 …

… This book has grown out of a course of lectures on elliptic functions, given in German, at the
Swiss Federal Institute of Technology, Zürich, during the summer semester of 1982. Its aim is …

… Elliptic Integrals of the three kinds to Jacobi's Amplitude, which is the argument of the Elliptic
Functions (… , sn, cn, dn), and also of Jacobi's functions Z, II, which replace the integrals of the …

… on elliptic generalizations of various beta integrals are reviewed. Firstly, a single variable
Askey-Wilson type integral describing an elliptic … integral defining an elliptic extension of the …

… We start from a brief technical introduction to the needed results on special functions and
discuss the physical systems they apply to in the following chapters. General theory of …

… ing an elliptic generalization of the Nassrallah-Ra.bman q-beta integral. It depends on five
… EC of a ratio of the Ruij&enaars elliptic gamma functiona depending on z and tm as another …

… As a solution to this problem, cryptography schemes based on the discrete logarithm problem
on elliptic curves are proposed. Now a day, many encryption and decryption schemes are …

… of (B) applied to elliptic differentials on Fermat curves, instead of … -function are isogenous
over Fq. Note that Deligne’s conjecture gives a connectionbetween gamma- and betafunction …

… Both of these identities are extensions of the beta function given as an integral on [0, oo),
and the sum contains a few of Jacobi's elliptic function identities. The gamma …

… for this function and its particular subcases are described. The known elliptic beta integrals
on root … are considered for the corresponding higher-order elliptic hypergeometric functions. …