
06166896
j
2013e.00610
Anghel, Vinicius Nicolae Petre
A use of symmetry: generalization of an integral identity found by M. L. Glasser.
Am. Math. Mon. 120, No. 1, 6269 (2013).
2013
Mathematical Association of America (MAA), Washington, DC
EN
I55
integral identity
Glasser's identity
$n$hemispherical surface
Zbl 1252.33012
doi:10.4169/amer.math.monthly.120.01.062
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, 302303 (1987)].