Jørgen Pedersen Gram: Difference between revisions
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'''Jørgen Pedersen Gram''' (June 27, 1850 – April 29, 1916) was a [[Denmark|Danish]] [[actuary]] and [[mathematician]] who was born in [[Nustrup]], Duchy of [[Schleswig]], [[Denmark]] and died in [[Copenhagen]], Denmark. |
'''Jørgen Pedersen Gram''' (June 27, 1850 – April 29, 1916) was a [[Denmark|Danish]] [[actuary]] and [[mathematician]] who was born in [[Nustrup]], Duchy of [[Schleswig]], [[Denmark]] and died in [[Copenhagen]], Denmark. |
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Important papers of his include ''On series expansions determined by the methods of least squares'', and ''Investigations of the number of primes less than a given number''. The |
Important papers of his include ''On series expansions determined by the methods of least squares'', and ''Investigations of the number of primes less than a given number''. The mathematical method that bears his name, the [[Gram–Schmidt process]], was first published in the former paper, in 1883.<ref>{{cite book|title=Linear Algebra|author=David Poole|pages=387|publisher=Thomson Brooks/Cole|date=2005|isbn=0534998453}}</ref> The [[Gramian matrix]] is also named after him. |
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For number theorists his main fame is the series for the [[Riemann zeta function]] (the leading function in [[Riemann]]'s exact [[prime-counting function]]). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of [[Ramanujan]] that uses the [[Bernoulli number]]s directly instead of the zeta function. |
For number theorists his main fame is the series for the [[Riemann zeta function]] (the leading function in [[Riemann]]'s exact [[prime-counting function]]). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of [[Ramanujan]] that uses the [[Bernoulli number]]s directly instead of the zeta function. |
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Revision as of 17:08, 7 June 2011
 | This article needs additional citations for verification. (October 2008) |
Jørgen Pedersen Gram (June 27, 1850 – April 29, 1916) was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark.
Important papers of his include On series expansions determined by the methods of least squares, and Investigations of the number of primes less than a given number. The mathematical method that bears his name, the Gram–Schmidt process, was first published in the former paper, in 1883.[1] The Gramian matrix is also named after him.
For number theorists his main fame is the series for the Riemann zeta function (the leading function in Riemann's exact prime-counting function). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of Ramanujan that uses the Bernoulli numbers directly instead of the zeta function.
Gram was the first mathematician to provide a systematic theory of the development of skew frequency curves, showing that the normal symmetric Gaussian error curve was but one special case of a more general class of frequency curves.[2]
He died after being struck by a bicycle.[3]
See also
- Gram matrix
- Logarithmic integral function
- Prime number
- Riemann-Siegel theta function which contain Gram points.
References
- ^ David Poole (2005). Linear Algebra. Thomson Brooks/Cole. p. 387. ISBN 0534998453.
- ^ Helen Mary Walker (1929). Studies in the History of Statistical Method: With Special Reference to Certain Educational Problems. The Williams & Wilkins Company. pp. 77, 81.
- ^ O'Connor, John J.; Robertson, Edmund F., "Jørgen Pedersen Gram", MacTutor History of Mathematics Archive, University of St Andrews
Bibliography
- Gram, J. P. (1884). "Undersøgelser angaaende Maengden af Primtal under en given Graeense". Det K. Videnskabernes Selskab. 2: 183–308.
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