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Bourget function

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The function which may be defined as a generalization of the integral representation of the Bessel functions

where is an integer and is a positive integer. The integration contour makes one counter-clockwise turn around the coordinate origin. In other words,

is a cylinder function of the first kind. So named after J. Bourget [1], who studied the function with a view to various applications in astronomy.

References

[1] J. Bourget, "Mémoire sur les nombres de Cauchy et leur application à divers problèmes de mécanique céleste" J. Math. Pures Appl. (2) , 6 (1861) pp. 32–54
[2] G.N. Watson, "A treatise on the theory of Bessel functions" , 1 , Cambridge Univ. Press (1952) pp. Chapt. 10
How to Cite This Entry:
Bourget function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bourget_function&oldid=32896
This article was adapted from an original article by V.I. Pagurova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article