WebIn a recent paper [H], we proved the "Mock Theta Conjectures". These are identities, stated by Ramanujan in his "lost notebook" JR2, pp. 19-20], involving two of the 5th order mock 0-functions. In fact, Ramanujan gave one such identity for each of the ten 5th order functions; as shown in [A-G1], these ten identities are all equivalent to the two proved in … Web20 de nov. de 2024 · These functions are related to a function H ( x, q), where x is usually q r or e 2 π i r for some rational number r. For this reason we refer to H as a “universal” mock θ -function. Modular transformations of H give rise to the functions K, K 1, K 2. The functions K and K 1 appear in Ramanujan's lost notebook.
[2202.03329] Mock theta functions and related combinatorics
WebIn this paper we obtain the transformations of Ramanujan's fifth and seventh order mock theta functions under the modular group generators + 1 and –1/, where q = e i. The transformation formulas ... Web2) and proved that 𝒟 5 ( 𝑞) is a mock theta function and called it of “2nd” order. He further showed that 𝒟 5 ( 𝑞) is a sum of two mock theta functions ℎ 1 ( 𝑞) and 𝜔 ( 𝑞) where ℎ 1 ( 𝑞) is of … optical express dundee
Mock Theta Functions - Wolfram Demonstrations Project
Web19 de mai. de 1999 · Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously, the author proved six of the eight tenth order mock theta function identities. It is the purpose of this paper to prove the fifth and sixth identities of … WebThe extended results allow us to produce Hecke type series for the fifth and seventh order mock theta functions. New results on the generating function for sums of three … Weborder mock theta functions. Previously the author proved the rst six of Ra-manujan’s tenth order mock theta function identities. It is the purpose of this paper to prove the seventh and eighth identities of Ramanujan’s tenth order mock theta function identities which are expressed by mock theta functions and a de nite integral. L. J. portis exchange