The cross section for muon pair productions by electrons scattering over photons, $sigma_{MPP}$, is calculated analytically in the leading order. It is pointed out that for the center-of-mass energy range, $s geq 5 m^{2}_{mu}$, the cross section for $sigma_{MPP}$ is less than $1 mu $b. The differential energy spectrum for either of the resulting muons is given for the purpose of high-energy neutrino astronomy. An implication of our result for a recent suggestion concerning the high-energy cosmic neutrino generation through this muon pair is discussed.
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