Γ2 (½)is more than just π
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For a fixed positive integer m, factorial m is defined byThe problem of finding a formula extending the factorial m! to positive real values of m was posed by D. Bernoulli and C. Goldbach and solved by Euler. In his letter of 13 October 1729 to Goldbach [1], Euler defined a function (which we denote as Γ (x + 1)) by means ofand showed that Γ (m + 1) = m! for positive integers m. After that, Euler found representations for the so-called gamma function (1) in terms of either an infinite product or an improper integral. We refer the reader to the classical (and short) treatise [2] for a brief introduction and main properties of the gamma function.
2018 ◽
Vol 107
(02)
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pp. 272-288
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1961 ◽
Vol 5
(1)
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pp. 35-40
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2010 ◽
Vol 81
(2)
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pp. 177-185
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1962 ◽
Vol 13
(2)
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pp. 143-152
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2007 ◽
Vol 03
(01)
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pp. 43-84
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1995 ◽
Vol 51
(1)
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pp. 87-101
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1974 ◽
Vol 17
(2)
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pp. 193-199
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