This paper considers the theory of continuous wavelet transform associated with the \(\mu \) th order Mehler-Fock transform ( \(\mu \) MFT) and presents several fundamental operational results. In particular, we derive Parseval-type and Plancherel-type relations and establish a reconstruction formula for the Mehler-Fock continuous wavelet transform (MFCWT). Furthermore, we investigate the composition of two wavelet transforms and obtain the corresponding Parseval-type and Plancherel-type identities. Unlike classical Fourier-based wavelet transforms, the present approach is developed in the setting of an index transform and provides a new analytical framework associated with the \(\mu \) MFT. The obtained results may be useful for further studies in integral transforms, harmonic analysis, and related wavelet frameworks.
