Das, Sabuj and Mohajan, Haradhan (2014): Generating Functions for β1(n) and β2(n). Published in: International Journal of Scientific Knowledge , Vol. 5, No. 3 (30 July 2014): pp. 2735.

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Abstract
This paper shows how to prove the two Theorems, which are related to the terms β1(n) and β2(n) respectively Theorem: N(0,5,5n+1)= β1(n)+N (5,5,5n+1) and Theorem: N(1,5,5n+1)= β2(n)+ N(2,5,5n+2).
Item Type:  MPRA Paper 

Original Title:  Generating Functions for β1(n) and β2(n) 
English Title:  Generating Functions for β1(n) and β2(n) 
Language:  English 
Keywords:  Generating functions, Jecobi’s triple product 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60  General 
Item ID:  83046 
Depositing User:  Haradhan Kumar Mohajan 
Date Deposited:  02 Jan 2018 23:06 
Last Modified:  02 Jan 2018 23:06 
References:  1. Andrews, G.E. and Garvan, F.G. (1989). Ramanujan’s “Lost” Notebook VI: The Mock Theta Conjectures, Advances in Mathematics, 73: 242–255. 2. Andrews, G.E. (1979). An Introduction to Ramanujan’s “Lost” Notebook, American Mathematical Monthly, 86: 89–108. 3. Garvan, F.G. (1986). Generalizations of Dyson’s Rank, Ph. D. Thesis, Pennsylvania State University. 4. Garvan, F.G. (1979). Partitions Yesterday and Today, New Zealand Mathematical Society, Wellington. 5. Watson, G.N. (1937). The Mock Theta Functions (2), Proceedings of the London Mathematical Society, 42: 274–304. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/83046 