Double Integral

A double integral is a two-fold multiple integral.

Examples of definite double integrals evaluating to simple constants include

			(1)
			(2)
			(3)
			(4)

where  is Catalan's constant (Borwein et al. 2004, pp. 48-49), and

(5)

where  is the Euler-Mascheroni constant (Sondow 2003, 2005; Borwein et al. 2004, pp. 48-49).

REFERENCES:

Borwein, J.; Bailey, D.; and Girgensohn, R. Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters, 2004.

Sondow, J. "Criteria for Irrationality of Euler's Constant." Proc. Amer. Math. Soc. 131, 3335-3344, 2003. http://arxiv.org/abs/math.NT/0209070.

Sondow, J. "Double Integrals for Euler's Constant and  and an Analog of Hadjicostas's Formula." Amer. Math. Monthly112, 61-65, 2005.