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The changes in characteristics of Bose condensation of ideal Bose gas due toan external generic power law potential $U=\sum_{i=1} ^d c_i|\frac{x_i}{a_i}|^{n_i}$ are studied carefully. Detailed calculation of Kim$et$ $al.$ (S. H. Kim, C. K. Kim and K. Nahm, J Phys. Condens. Matter 11 10269(1999).) yielded the hierarchy of condensation transitions with changingfractional dimensionality. In this manuscript, some theorems regarding specificheat at constant volume $C_V$ are presented. Careful examination of thesetheorems reveal the existence of hidden hierarchy of the condensationtransition in trapped systems as well.

Investigation of Bose condensation in ideal Bose gas trapped under generic power law potential in $d$ dimension