Śrīnivāsa Rāmānujan: Difference between revisions
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'''Infinite Series for π''' : Śrīnivāsa Rāmānujan discovered infinite series for π in1910 . The series <math>\frac{1}{\pi} = \frac{2\sqrt{2}}{9801}\sum_{k=0}^\infty \frac{(4k\mid)(1103+26390k)}{(k)^4\, 396^{4k}} </math> | '''Infinite Series for π''' : Śrīnivāsa Rāmānujan discovered infinite series for π in1910 . The series <math>\frac{1}{\pi} = \frac{2\sqrt{2}}{9801}\sum_{k=0}^\infty \frac{(4k\mid)(1103+26390k)}{(k)^4\, 396^{4k}} </math> | ||
'''Theory of Equations''' : He derived the formula to solve biquadratic equations. | |||
'''Asymptotic Formula''' : He worked on partition of numbers. Using partition function p(n) derived a number of formulae in order to calculate the partition of numbers | |||
<math>p(n)\thicksim \frac{1}{4n\sqrt{3}} e^\pi\sqrt{\frac{2n}{3}} , n\rightarrow\infty </math> | |||
== See Also == | == See Also == | ||
[[श्रीनिवास रामानुजन्]] | [[श्रीनिवास रामानुजन्]] | ||
Revision as of 16:55, 7 November 2022
Śrīnivāsa Rāmānujan | |
|---|---|
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| जन्म | 22 December 1887 Erode |
| मर गया | 26 April 1920 (aged 32) Kumbakonam |
| पुरस्कार | Fellow of the Royal Society |
Śrīnivāsa Rāmānujan born Śrīnivāsa Rāmānujan Aiyangar, (22 December 1887 – 26 April 1920)[1] was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable.
The number 1729. It is known as Rāmānujan number. It is the smallest number which can be expressed as the sum of two cubes in two different ways.
1729 = 13+ 123= 93+ 103
Contributions
Rāmānujan number :The number 1729. It is known as Rāmānujan number. It is the smallest number which can be expressed as the sum of two cubes in two different ways.
1729 = 13+ 123= 93+ 103
Infinite Series for π : Śrīnivāsa Rāmānujan discovered infinite series for π in1910 . The series
Theory of Equations : He derived the formula to solve biquadratic equations.
Asymptotic Formula : He worked on partition of numbers. Using partition function p(n) derived a number of formulae in order to calculate the partition of numbers
