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A Use of Symmetry: Generalization of an Integral Identity Found by M. L. Glasser

Vinicius Nicolae Petre Anghel
The American Mathematical Monthly
Vol. 120, No. 1 (January 2013), pp. 62-69
DOI: 10.4169/amer.math.monthly.120.01.062
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.01.062
Page Count: 8
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A Use of Symmetry: Generalization of an Integral Identity Found by M. L. Glasser
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Abstract

Abstract The integral identity found by M. L. Glasser [3] 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 J. R. Bottiger [2].

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