Properties of Certain Bilateral Mock Theta Functions-IV
Keywords:
Mock theta functions, bilateral mock theta functions, Lerch transcendent, F-function.Abstract
Bilateral mock theta functions were obtained and studied in [23]. We express them in terms of Lerch's transcendental function f(x, ?; q, p) We also express some bilateral mock theta functions as sum of other mock theta functions. We generalize these functions and show that these generalizations are F_q functions. We give an integral representation for these generalized functions.
References
- Y. S. Choi, Tenth order mock theta functions in Ramanujan's lost note book, Inventiones Mathematicae 136 (1999), 497-569.
- S.D. Prasad, Certain extended mock theta functions and generalized basic hypergeometric transformation, Math Scand 27 (1970), 237-244.
- S. Ramanujan, Collected Papers, Cambridge University Press (1927), reprinted by Chelsea New York, 1960.
- R.P. Agarwal, Mock theta functions-An analytical point of view, Proc. Nat. Acad. Sci. India. 64(A.I) (1994), 95-106.
- R. J. McIntosh, Second order mock theta functions, Canadian Mathematical Bulletin 50 (2)? (2007), 284-290.
- N. J. Fine, Basic hypergeometric series and applications Mathematical Surveys & Mono Graphs, Providence, R.I Amer. Math. Soc.? 27, 1988.
- M. Lerch. ,Nov analogie rady theta a nekte zvltn hypergeometrick rady Heineovy. Rozpravy? 3? (1893), 1?10.
- M Ahmad, On the Behavior of Bilateral Mock Theta Functions-I, Algebra and Analysis: Theory and Application, Narosa Publishing House Pvt Ltd, New Delhi, 2015, 259-273.
- M Ahmad and Shahab Faruqi,Some Bilateral Mock Theta Functions and Their Lerch Representations,The Aligarh Bulletin of Mathematics,Vol 34,Numbers 1-2(2015) 75-92 .
- M Ahmad and Shahab Faruqi,Properties of Certain Bilateral Mock Theta Functions, Accepted for publication in GAMS Journal of Mathematics and Mathematical Biology.
- L.A. Dragonette, Some asymptotic formulae for the mock theta series of Ramanujan, Trans. Amer. Math. Soc.? 72? (1952), 474-500.
- K. Bringmann, K. Hikami and Jeremy Lovejoy, On the modularity of the unified WRT invariants of certain Seifert manifolds, Advances in Applied Mathematics 46(1) (2011), 86-93.
- K. Hikami, Mock (false) theta functions as quantum invariants, Regular and Chaotic Dynamics, 10? (2005), 509-530.
- K. Hikami, Transformation formulae of the 2nd order mock theta function, Lett. Math. Phys.? 75(1) (2006), 93-98.
- G.E. Andrews and D. Hickerson, The sixth order mock theta functions, Adv. Maths 89 (1991), 60-105.
- G. E. Andrews, q-orthogonal polynomials, Roger-Ramanujan identities and mock theta functions, Proc. Steklov Institute of Math. 276(1)? (2012), 21-32.
- G. Gasper and M. Rahman, Basic Hypergeometric Series, 2nd ed, Cambridge University Press Cambridge (UK), 2004.
- G. N. Watson, The final Problem: An account of the mock theta functions, Journal of the London Math, Soc. 11 (1936), 55-80.
- G. N. Watson, The Mock Theta Functions (2), Proc. London Math, Soc. 42 (1937), 274-304.
- D. P. Shukla and M. Ahmad, Bilateral mock theta functions of order seven, Math Sci. Res. J. 7(1) (2003), 8-15.
- D. P. Shukla and M. Ahmad, On the behaviour of bilateral mock theta functions of order seven, Math Sci. Res. J. 7(1)? (2003), 16-25.
- D. P. Shukla M. Ahmad, Bilateral mock theta functions of order eleven, Proc. Jang Jeon Math Soc. 6(1) (2003), 59-64.
- D. P. Shukla and M. Ahmad, Bilateral mock theta functions of order thirteen, Proc. Jang Jeon Math Soc.? 6(2) (2003), 167-183.
- D. P. Shukla and M. Ahmad, Bilateral mock theta functions of order 2r+1 and their behaviour on the unit circle, GANITA Vol 60 , No. 1,(2009),27-56.
- Clifford Truesdell. An essay toward a unified theory of special functions, 18 Princeton university press, 1948.
- Bhaskar Srivastava, Certain bilateral basic hypergeometric transformations and mock theta functions, Hiroshima Maths J.? 29? ?(1999), 19-26.
- Bhaskar Srivastava, A study of bilateral forms of the mock theta functions of order eight, Journal of the Chungcheon Math Soc.? 18(2)? (2005), 117-129
- Bhaskar Srivastava, A mock theta function of second order, International Journal of Mathematics and Mathematical Sciences 2009 (2010), 1-15.
- Bhaskar Srivastava, A study of bilateral new mock theta functions, American journal of Mathematics and Statistics? 2(4) (2012), 64-69.
- B. Gordon and R. J. McIntosh, Some eight order mock theta functions, Journal of the London Math, Soc.? 62(2)?? (2000), 321-335.
- Anju Gupta, On certain Ramanujan's mock theta functions, Proc. Indian Acad. Sci. 103(1993), 257-267.
Downloads
Published
Issue
Section
License
Copyright (c) IJSRST

This work is licensed under a Creative Commons Attribution 4.0 International License.