A remark on ‘The beta-gamma function identity via Taylor's formula’ by Chen and Chen

An elementary proof of the beta-gamma function identity is presented by Chen and Chen [Chen, H.-C., & Chen, H. L. (2025). The beta-gamma function identity via Taylor's formula. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2025.2573176]. In this note we remark that the limiting arguments in Section 2.3 and Appendix of Chen and Chen [Chen, H.-C., & Chen, H. L. (2025). The beta-gamma function identity via Taylor's formula. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2025.2573176] can be considerably simplified. Our alternative arguments make their proof much more accessible to students in elementary single-variable calculus classes.