Śrīnivāsa Rāmānujan - Revision history

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Indicwiki: 22 revisions imported from :alpha:Śrīnivāsa_Rāmānujan

2022-11-29T03:32:00Z

22 revisions imported from alpha:Śrīnivāsa_Rāmānujan

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alpha>Ramamurthy S: /* References */

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References

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	[[Category:Indian Mathematicians]]		[[Category:Indian Mathematicians]]
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alpha>Abhishek: Abhishek moved page Srinivasa Ramanujan to Śrīnivāsa Rāmānujan without leaving a redirect

2022-11-28T09:44:14Z

Abhishek moved page Srinivasa Ramanujan to Śrīnivāsa Rāmānujan without leaving a redirect

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alpha>Ramamurthy S: External Links added

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	== External Links ==		== External Links ==
	[https://mathshistory.st-andrews.ac.uk/Biographies/Ramanujan/ Ramanujan]
			* [https://mathshistory.st-andrews.ac.uk/Biographies/Ramanujan/ Ramanujan]

			* [https://ia903003.us.archive.org/30/items/arxiv-math0003184/math0003184.pdf Life and work of the Mathemagician Srinivasa Ramanujan]

	== References ==		== References ==

alpha>Ramamurthy S: External Links added

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External Links added

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	== See Also ==		== See Also ==
	[[श्रीनिवास रामानुजन्]]		[[श्रीनिवास रामानुजन्]]

			== External Links ==
			[https://mathshistory.st-andrews.ac.uk/Biographies/Ramanujan/ Ramanujan]

	== References ==		== References ==

alpha>Ramamurthy S: /* Contributions */

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Contributions

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	1729 = 1<sup>3</sup>+ 12<sup>3</sup>= 9<sup>3</sup>+ 10<sup>3</sup>		1729 = 1<sup>3</sup>+ 12<sup>3</sup>= 9<sup>3</sup>+ 10<sup>3</sup>

	'''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'''<ref>{{Cite web\|title=Srinivasa Ramanujan's Contributions in Mathematics\|url=https://www.iosrjournals.org/iosr-jm/papers/Vol12-issue3/Version-4/O120304137139.pdf}}</ref> : 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]].		'''Theory of Equations''' : He derived the formula to solve biquadratic [[equations]].

alpha>Ramamurthy S: internal links added

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	}}		}}

	'''Śrīnivāsa Rāmānujan''' born '''Śrīnivāsa Rāmānujan Aiyangar''', (22 December 1887 – 26 April 1920)<ref>{{Cite web\|title=Śrīnivāsa Rāmānujan\|url=https://en.wikipedia.org/wiki/Srinivasa_Ramanujan}}</ref> 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.		'''Śrīnivāsa Rāmānujan''' born '''Śrīnivāsa Rāmānujan Aiyangar''', (22 December 1887 – 26 April 1920)<ref>{{Cite web\|title=Śrīnivāsa Rāmānujan\|url=https://en.wikipedia.org/wiki/Srinivasa_Ramanujan}}</ref> 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.

	== Contributions ==		== 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.		'''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 = 1<sup>3</sup>+ 12<sup>3</sup>= 9<sup>3</sup>+ 10<sup>3</sup>		1729 = 1<sup>3</sup>+ 12<sup>3</sup>= 9<sup>3</sup>+ 10<sup>3</sup>

	'''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.		'''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		'''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>		<math>p(n)\thicksim \frac{1}{4n\sqrt{3}} e^\pi\sqrt{\frac{2n}{3}} , n\rightarrow\infty </math>

alpha>Ramamurthy S: Content added

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Content added

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	*Top row represents the date of birth '''Rāmānujan'''		*Top row represents the date of birth '''Rāmānujan'''

			'''Ramanujan’s Congruences :'''

			He discovered the congruences

			<math>p(5n+4) \equiv 0(mod \ 5)</math>

	~~'''Ramanujan’s Congruences :'''~~		<math>p(7n+5) \equiv 0(mod \ 7)</math>

	~~He discovered the congruences~~

	<math>p(5n+4) \equiv 0(mod 5)		<math>p(11n+6) \equiv 0(mod \ 11),\forall n \in N</math>
	~~p(5n+4~~) \~~equiv 0(mod 5)~~
	~~p(5n+4)~~ \~~equiv 0(mod 5)~~</math>

	== See Also ==		== See Also ==

alpha>Ramamurthy S: /* See Also */

2022-11-10T07:18:17Z

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	* Sum of numbers of any diagonal is 139		* Sum of numbers of any diagonal is 139
	* Sum of corner numbers is 139		* Sum of corner numbers is 139
			*Top row represents the date of birth '''Rāmānujan'''