id: 06166896
dt: j
an: 2013e.00610
au: Anghel, Vinicius Nicolae Petre
ti: A use of symmetry: generalization of an integral identity found by M. L.
Glasser.
so: Am. Math. Mon. 120, No. 1, 62-69 (2013).
py: 2013
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: I55
ut: integral identity; Glasser’s identity; $n$-hemispherical surface
ci: Zbl 1252.33012
li: doi:10.4169/amer.math.monthly.120.01.062
ab: Summary: The integral identity found by {\it M. L. Glasser\/} [J. Phys. A,
Math. Theor. 44, No. 22, Article ID 225202, 5 p. (2011; Zbl
1252.33012)] is generalized using the permutation symmetry of
coordinates of an $n$-spherical surface simplex. The first calculation
technique is simple to apply, but the second technique allows further
generalization of M. L. Glasser’s identity. Analogous results are
discussed for the $n$-hemispherical surface of the unit $n$-sphere and
for the entire surface of the $n$-sphere. The $n$-sphere surface result
is used to generalize M. L. Glasser’s solution to a problem proposed
by {\it J. R. Bottiger\/} and {\it D. K. Cohoon\/} [“A normalization
constant", SIAM Review 29, 302‒303 (1987)].
rv: