@inproceedings{Nakatsuka:2023vb, author = "Nakatsuka, Takao", title = "{Formulae to predict the excess-path-length distribution of cascade-shower electrons}", doi = "10.22323/1.444.0681", booktitle = "Proceedings of 38th International Cosmic Ray Conference {\textemdash} PoS(ICRC2023)", year = 2023, volume = "444", pages = "681" }