Characteristic energy-dissipating functions of muon penetrating through matters

The characteristic energy-dissipating functions of muon corresponding to positron-electron pair production, bremsstrahlung, and photonuclear interactions are expressed in series-expansions, to investigate transmission properties of muon effectively by analytical methods developed in the cascade shower theory. Accuracies of the new expression are examined by comparing one of the characteristic functions with that derived by the traditional analytical method. We apply the new-obtained characteristic functions to derive the survival probability of muon and compare the result with that of electron, discussing the discrepancies between the both.