for
an even integer is also considered by Gray (1997, p. 292) and is a special case
of the superellipsoid.
The volume of the case
is given by
(3)
(4)
where
(5)
is the real
part of
and
is a Bessel function of the first kind
(E. W. Weisstein and M. Trott, pers. comm., Nov. 9, 2008), which
can probably be expressed in closed form in terms of bivariate hypergeometric functions.
.
)
an even integer is also considered by Gray (1997, p. 292) and is a special case
of the superellipsoid.
is given by
![int_0^infty-(pi^2)/(16sqrt(2))R{((-1)^(5/8))/(t^(7/4))[(-1)^(1/4)e^(it/8)t^(3/4)×[(-1)^(3/4)J_(1/4)(t/8)-J_(-1/4)(t/8)]^3+(12sqrt(t)Gamma(1/4))/(pi^2)+(2(1+i)Gamma^3(1/4))/(pi^3)]}dt](/images/equations/GoursatsSurface/Inline13.svg)
![R[z]](/images/equations/GoursatsSurface/Inline14.svg)
is the real
part of 
and 
is a Bessel function of the first kind
(E. W. Weisstein and M. Trott, pers. comm., Nov. 9, 2008), which
can probably be expressed in closed form in terms of bivariate hypergeometric functions.
