In some papers, the dilations and translations of a wavelet function is written as follows:
$$\psi_{j,k}=\frac {1}{\sqrt {2^j}} \psi\left({2^{-j}t-k}\right),\quad\text{where $j$ and $k$ are integers}$$
However, in some literature, the above formula is written in a different way:
$$\psi_{j,k}=\ {\sqrt {2^j}} \psi\left({2^{j}x-k}\right), \quad\text{where $j$ and $k$ are integers}$$
Are these two formula equivalent?