Bourget function

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