The Pentagonal Number Theorem and All That
... follows easily by induction, if one multiplied many factors. The remainder of the series I do not see. This can be shown in a most pleasant investigation, together with tranquil pastime and the endurance of pertinacious labor, all three of which I lack.” Euler mentions the theorem many more times ov ...
... follows easily by induction, if one multiplied many factors. The remainder of the series I do not see. This can be shown in a most pleasant investigation, together with tranquil pastime and the endurance of pertinacious labor, all three of which I lack.” Euler mentions the theorem many more times ov ...
Ramanujan, Robin, highly composite numbers, and the Riemann
... Here [19] is Robin’s paper, which he published three years before learning of Ramanujan’s Theorem. However, a reader of [16] who neglects to look up [19] in the References is left with the misimpression “that the above relation with n0 = 5040 is equivalent to the Riemann hypothesis” was proven after ...
... Here [19] is Robin’s paper, which he published three years before learning of Ramanujan’s Theorem. However, a reader of [16] who neglects to look up [19] in the References is left with the misimpression “that the above relation with n0 = 5040 is equivalent to the Riemann hypothesis” was proven after ...
historical notes - Indian National Science Academy
... Continued fractions Ramanujan’s Notebooks contain almost 200 entries about continued fractions. Bruce C. Berndt rightly remarked, ‘It seemed to us that no person in the history of mathematics possessed the skill that Ramanujan had in determining continued fractions for various functions or finding c ...
... Continued fractions Ramanujan’s Notebooks contain almost 200 entries about continued fractions. Bruce C. Berndt rightly remarked, ‘It seemed to us that no person in the history of mathematics possessed the skill that Ramanujan had in determining continued fractions for various functions or finding c ...
Ramanujan, taxicabs, birthdates, zipcodes and twists
... Ramanujan’s notebooks. Bruce has devoted most of his professional career to undertaking the daunting task of proving many of Ramanujan’s identities (written in notebooks without proofs), but to my surprise his fascination with Ramanujan has profoundly impacted his life outside mathematics. Sonja, Br ...
... Ramanujan’s notebooks. Bruce has devoted most of his professional career to undertaking the daunting task of proving many of Ramanujan’s identities (written in notebooks without proofs), but to my surprise his fascination with Ramanujan has profoundly impacted his life outside mathematics. Sonja, Br ...
A prime number (or a prime) is a natural number
... A BRIEF… Srinivasa Ramanujan (Tamil:ஸ்ரீனிவாஸ ராமானுஜன்; 22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fra ...
... A BRIEF… Srinivasa Ramanujan (Tamil:ஸ்ரீனிவாஸ ராமானுஜன்; 22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fra ...
ramanujan
... Most of us know his story, but love to hear the tale yet again. Ramanujan was born on 22 December 1887 in Erode. He showed an early penchant for mathematics, mastering trigonometry and proving his own theorems by the age of 12. By the age of 17, Ramanujan conducted his own mathematical research on B ...
... Most of us know his story, but love to hear the tale yet again. Ramanujan was born on 22 December 1887 in Erode. He showed an early penchant for mathematics, mastering trigonometry and proving his own theorems by the age of 12. By the age of 17, Ramanujan conducted his own mathematical research on B ...
Contribution of Indian Mathematicians
... (1) Aryabhatta was born in 476 A.D. Kusumpur, India.He was the first in the line of great mathematicians from the classical age of Indian Mathematics and Astronomy. (2) His famous work are the” Aryabhatiya “and the”Arya‐siddhanta”.The Mathematical part of the Aryabhatiya covers arithmetic. algeb ...
... (1) Aryabhatta was born in 476 A.D. Kusumpur, India.He was the first in the line of great mathematicians from the classical age of Indian Mathematics and Astronomy. (2) His famous work are the” Aryabhatiya “and the”Arya‐siddhanta”.The Mathematical part of the Aryabhatiya covers arithmetic. algeb ...
Srinivasa Ramanujan
Srinivasa Ramanujan Iyengar FRS (pronunciation: /sriː.ni.vaː.sə raː.maː.nʊ.dʒən/) (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians. When his skills became apparent to the wider mathematical community, centred in Europe at the time, he began a famous partnership with the English mathematician G. H. Hardy. He rediscovered previously known theorems in addition to producing new work.During his short life, Ramanujan independently compiled nearly 3900 results (mostly identities and equations). Nearly all his claims have now been proven correct, although some were already known. 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.