## Resonance of Ramanujan's mathematics, Volume 3The Present Volume Is The Third Of The Series Resonance Of Ramanujans Mathematics Written By The Author. The First Two Volumes Were Published In 1996. As In The First Two Volumes, This Volume Contains Five Chapters. The Topics Selected For This Volume Are Continued Fractions -Comprising Of The First Three Chapters, Riemann Zeta Function And The Fifth Chapter Is A Masterly And An Up-To-Date Article On Elliptic Functions On Alternative Bases By Prof. S. Bhargava (Mysore), Reprinted From The Proc. Nat. Acad. Sci (India) 68 (1998), By The Kind Permission Of The Chief Editor. The Chapters On Continued Fractions, A Topic In Which Ramanujan Has Been, Probably, At His Best, Are Aimed At Giving The Most Recent Developments In That Topic And Should Prove Useful To The Research Workers In A Better Understanding Oframanujans Work And In Further Extending His Results. The Fourth Chapter On Riemann Zeta Function, Which Is Of Importance In The Theory Of Numbers, Asymptotic Theory, And Series Transformations Etc., Gives An Idea Of The Diverse Nature Of Topics In Which Ramanujan Has Made Valuable Contribution.The Last Chapter Reprinted From The Proc. Nat. Acad. Sci. (India) 68 (1998) Gives An Up-To-Date And Thorough Discussion Of Elliptic Function Theory On Alternative Bases.This Volume Should Prove To Be A Valuable Asset For Researchers Working Onramanujans Mathematics. Each Chapter, As Before, Is Followed By An Up-To-Date And Comprehensive Bibliography And Provides An Independent Reading. |

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### Contents

Ramanujan and Continued fractionI | 1 |

Continued fractions and the generalised | 31 |

Certain special cases of continued fraction identities | 44 |

Copyright | |

7 other sections not shown

### Common terms and phrases

abcq Adiga Andrews et.al asymptotic expansion ax ax basic hypergeometric functions basic hypergeometric series Bauer-Muir transformation Berndt B2 Bernoulli numbers Bhargava et.al class invariants complex numbers continued fraction identities continued fraction representations continued fractions found convergence de/abc defined derived discussed end of R2 Entry 12 Entry 35 Entry 40 Euler's evaluations follows gamma functions generalisation gives Gn and gn Gupta Hahn polynomials hypergeometric series Jacobi's Jacobian elliptic functions Lemma Masson modular equations modular forms negative integer notation number of continued obtained orthogonal polynomials polynomials portion of Ramanujan's positive integer Proc proof of Entry quotient Ramanathan Ramanujan Ramanujan's continued fraction Ramanujan's Mathematics Ramanujan's Notebooks recurrence relations replacing Riemann Zeta function Rogers-Ramanujan continued fraction S.N. Singh series and continued simplification singular moduli theorem theory of elliptic theory of signature theta three-term contiguous relations unorganised portion Watson Weierstrassian well-known XII of R2