Sums of Series of Rogers Dilogarithm Functions
نویسندگان
چکیده
Some sums of series of Rogers dilogarithm functions are established by Abel’s functional equation.
منابع مشابه
A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities
We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler measures. Several of these results generalize formulas due to Condon and Laĺın. As a corollary, we also obtain three q-series expansions for the dilogarithm.
متن کاملNote on Dilogarithm Identities from Nilpotent Double Affine Hecke Algebras
Recently Cherednik and Feigin [arXiv:1209.1978] obtained several Rogers–Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA). These identities further led to a series of dilogarithm identities, some of which are known, while some are left conjectural. We confirm and explain all of them by showing the connection with Y -systems associated with (untwisted and twiste...
متن کاملTwo-dimensional Series Evaluations via the Elliptic Functions of Ramanujan and Jacobi
We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers–Ramanujan continued fraction play central roles in our evaluations.
متن کاملDilogarithm in Integrable Systems
We discuss some curious aspects of the Rogers dilogarithm appearing in integrable systems in two dimensions.
متن کاملA-D-E Polynomial and Rogers–Ramanujan Identities
We conjecture polynomial identities which imply Rogers–Ramanujan type identities for branching functions associated with the cosets (G)l−1⊗(G )1/(G )l, with G=An−1 (l ≥ 2), Dn−1 (l ≥ 2), E6,7,8 (l = 2). In support of our conjectures we establish the correct behaviour under level-rank duality for G=An−1 and show that the A-D-E Rogers–Ramanujan identities have the expected q → 1− asymptotics in t...
متن کامل