Ramanuj

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Rāmānuja (c. 1017 – c. 1137) Rāmānuja ( ācārya), the eleventh century South Indian philosopher, is the chief proponent of Viśiṣṭādvaita, which is one of the three main forms of the Orthodox Hindu philosophical school, Vedānta. As the prime philosopher of the Viśiṣṭādvaita tradition, Rāmānuja is one of the Indian philosophical tradition’s most important and influential figures. He was the first Indian philosopher to provide a systematic theistic interpretation of the philosophy of the Vedas, and is famous for arguing for the epistemic and soteriological significance of bhakti, or devotion to a personal God. Unlike many of his contemporaries, Rāmānuja defended the reality of a plurality of individual persons, qualities, values and objects while affirming the substantial unity of all. On some accounts, Rāmānuja’s influence on popular Hindu practice is so vast that his system forms the basis for popular Hindu philosophy. His two main philosophical writings (the Śrī Bhāṣya and Vedārthasaṅgraha) are amongst the best examples of rigorous and energetic argumentation in any philosophical tradition, and they are masterpieces of Indian scholastic philosophy. Table of Contents • • • • • • • • • • • • • • Brahman and Ātman • • • • • • Bhakti • • • • • Gadyas • • • • On traditional accounts, Rāmānuja lived the unusually long life of 120 years (twice the average lifespan at the time), from 1017 to 1137 C.E., though recent scholarship places his life between 1077 to 1157 C.E., with a life...

Registration Link for Ramanujan Talent Search Test in Mathematics-2022 Olympiad for Classes 6 to 12 conducted by Bihar Council on Science and Technology,Patna & Bihar Mathematical Society. Registration fee : Nil Last date for Registration - 03.12.2022. Admit card download from - 08.12.2022. Date of Examination - 11.12.2022. Publication of Result - 14.12.2022. Felicitation programme - 22.12.2022 SRTSTM winners will be awarded Laptop, Cash Prizes, Certificates and Medals. Registration details is here : Registration Link : Download admit card for Srinivasa Ramanujan Talent Search Test in Mathematics-2022 : Result of Srinivasa RamanujanTalent SearchTest in Mathematics-2022

On January 16, 1913, a letter revealed a genius of mathematics. The missive came from Madras, a city – now known as Chennai – located in the south of India. The sender was a young 26-year-old clerk at the customs port, with a salary of £20 a year, enclosing nine sheets of formulas, incomprehensible at first sight. “Dear Sir, I have no University education but I have undergone the ordinary school course. I have made special investigation of divergent series in general and the results I get are termed by the local mathematicians as startling,” began the writing signed by S. Ramanujan. A century later, the legacy of this Indian genius continues to influence mathematics, physics or computation. The Indian mathematician Srinivasa Ramanujan. Credit: Wikimedia Commons The renowned It contained 120 formulas among which he identified one for knowing how many prime numbers there are between 1 and a certain number, and others that allowed one to calculate quickly the infinite decimals of the number pi. In some cases, Ramanujan had unwittingly arrived at conclusions already reached by western mathematicians, such as one of Bauer’s formulas for the decimals of pi, but many other formulas were entirely new. The formulas came alone, isolated, without formal demonstrations or statements. This lack of methodology almost led Hardy to throw the letter into the rubbish. However, in the end he concluded that: “They must be true because, if not, no one would have had the imagination to invent t...

The result is stated as follows: If a complex-valued function f ( x ) . A multivariate integral may assume this form. :8 ∫ 0 ∞ ⋯ ∫ 0 ∞ ∑ n 1 , … , n S = 0 ∞ φ ( n 1 ⋯ n S ) ∏ j = 1 S ( ( − 1 ) n j n j ! ) ∏ j = 1 M ( x j ) ( − c j + a j 1 ⋅ n 1 + ⋯ + a j S ⋅ n S − 1 ) d x 1 ⋯ d x M ( ∑ k = 1 P u k ) ∓ d → ∑ n 1 , … , n P = 0 ∞ φ n 1 , … , n P ∏ k = 1 P u k n k ⟨ ± d + ∑ j = 1 P n j ⟩ Γ ( ± d ) ( B.5) • Each bracket series has an index defined as index=number of sums−number of brackets. • Among all bracket series representations of an integral, the representation with a minimal index is preferred. :984 Solve linear equations [ ] • The array of coefficients a j k . ( B.8) • These rules apply. :985 • A series is generated for each choice of free summation parameters, . • Series converging in a common region are added. • If a choice generates a • A bracket series of negative index is assigned no value. • If all series are rejected, then the method cannot be applied. • If the index is zero, the formula ( det | A | − 1 ) ⋅ ∫ 0 ∞ ⋯ ∫ 0 ∞ ∑ n 1 , … , n S = 0 ∞ φ ( n 1 ⋯ n S ) ∏ j = 1 S ( ( − 1 ) n j n j ! ) ∏ j = 1 M ( y j ) − n j ∗ + n j − 1 d y 1 ⋯ d y M ( B.12) • The number of brackets (B) equals the number of integrals (M) ( :14 Example [ ] • The bracket integration method is applied to this integral. ∫ 0 ∞ x 3 / 2 ⋅ e − x 3 / 2 d x References [ ] • Berndt, B. (1985). Ramanujan's Notebooks, PartI. New York: Springer-Verlag. • ^ a b c d González, Iván; Moll, V.H.; Schmid...