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A footnote to the theory of double integrals

Published online by Cambridge University Press:  23 January 2015

Juan Pla
Juan Pla*
Affiliation:
315 rue de Belleville, 75019 Paris, France
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Extract

The probability integral theorem, which states that

is on the record for having enticed numerous mathematicians to find alternative proofs for it, over a period of more than two centuries, till recent times (for a few recent references see [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]). The most popular demonstration (attributed to the French mathematician Poisson; see [11], in references of [12]), the one found in almost all textbooks, relies on the double integral

(taken over the upper-right quarter of the Cartesian plane) obtained by squaring the probability integral. By resorting to polar coordinates and writing down the above integral as:

the value of the probability integral is obtained by taking the square root of the result on the right-hand side of this latter relation.

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 530 , July 2010 , pp. 262 - 269
Copyright
Copyright © The Mathematical Association 2010

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References

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