Bourget Function

The function defined by the contour integral

where  denotes the contour encircling the point  once in a counterclockwise direction. It is equal to

(Watson 1966, p. 326).

REFERENCES:

Bourget, J. "Mémoire sur les nombres de Cauchy et leur application à divers problèmes de mécanique céleste." J. de Math. 6, 33-54, 1861.

Giuliani, G. "Alcune osservazioni sopra le funzioni spheriche di ordine superiore al secondo e sopra altre funzioni che se ne possono dedurre (April, 1888)." Giornale di Mat. 26, 155-171, 1888.

Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, p. 465, 1988.

Watson, G. N. "The Functions of Bourget and Giuliani." §10.31 in A Treatise on the Theory of Bessel Functions, 2nd ed.Cambridge, England: Cambridge University Press, pp. 326-327, 1966.