WebOct 1, 2024 · Mock theta functions can be represented by Eulerian forms, Hecke-type double sums, Appell–Lerch sums, and Fourier coefficients of meromorphic Jacobi forms. In view … WebOct 1, 2024 · Mock theta functions can be represented by Eulerian forms, Hecke-type double sums, Appell–Lerch sums, and Fourier coefficients of meromorphic Jacobi forms. In view …

A Survey of Classical Mock Theta Functions SpringerLink

Web3. Mock theta functions and partition ranks “The mock theta-functions give us tantalizing hints of a grand synthesis still to be dis-covered. Somehow it should be possible to build … WebRamanujan’s first example of a mock theta function is the Eulerian series 2 X X qn (12) f (q) = 1 + a (n)qn = 1 + , (1 + q)2 (1 + q2)2 ··· (1 + qn)2 n≥1 n≥1 which appears deceptively … early consideration

Some new mock theta functions - ResearchGate

WebGenerating Functions and Congruences for Some Partition Functions Related to Mock Theta Functions Nilufar Mana Begum A partition λ = (λ 1 , λ 2 , • • • , λ k ) of a positive integer n is … WebDec 11, 2024 · Hence, in the example given here. (7) In the above, implies summation over both m and n from − ∞ to ∞, excluding the case when are simultaneously zero. This removes the “1” in front of Equations (2) and (3). Thus, consider. (8) The sums over m and n on the RHS of (6) are completely independent of one another. We have. WebNew Mock Theta Function Identities. In his last letter to Hardy, Ramanujan defined ten mock theta functions of order 5 and three of order 7. He stated that the three mock theta … c# start 2 threads at the same time