Webb5 aug. 2011 · @article{Baruah2011AnaloguesOR, title={Analogues of Ramanujan’s partition identities and congruences arising from his theta functions and modular equations}, author={Nayandeep Deka Baruah and Kanan Kumari Ojah}, journal={The Ramanujan Journal}, year={2011}, volume={28}, pages={385 - 407} } Nayandeep Deka Baruah, Kanan … WebbThe Ramanujan identities for powers of the prime 7; 7. Completion of the proof for powers of 7. Index. (CHEL/337.H Modular Functions of One Variable IV - Sep 24 2024 Monthly Catalog of United States Government Publications - Apr 07 2024 Theta Functions, Bowdoin 1987 - Mar 31 2024 The 1-2-3 of Modular Forms - Oct 14 2024
sequences and series - A formula for Ramanujan
WebbFollowing Ramanujan's work on modular equations and approximations of π, there are formulas for 1/π of the form Following Ramanujan's work on modular equations and approximations of π, there are formulas for 1/π of the form ∑ k = 0 ∞ ( 1 2 ) k ( 1 d ) k ( d - 1 d ) k k ! 3 ( a k + 1 ) ( λ d ) k = δ π for d=2,3,4,6, where łd are singular values that … Webb3 aug. 2024 · The classical Jacobian theta-function is defined as The series is convergent in where We are interested in the theta-function with a fixed value such that is a holomorphic function on Let and Functional Equation of the Theta-Series Proof We have for by the example above. For we get with such that the Poisson summation with yields … how to give feedback to students examples
Srinivasa Ramanujan - Wikipedia
Webb22 dec. 2024 · He stated results that were both original and highly unconventional, such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research. The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work. Webb4 sep. 2016 · Abstract. We define a product for any positive real numbers and involving Ramanujan's theta-functions and which is analogous to Ramanujan's remarkable product of theta-functions recorded by Ramanujan (1957) and study its several properties. We prove general theorems for the explicit evaluations of and find some explicit values. As … WebbMany were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of … johnsons klear floor shine