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In this note we study the possible connection between functions appearing indiagrammatic expansion and the conformal correlator expansion. To study theconnection we propose a generating function which can be expanded to constructa basis. This basis can be utilized to expand, I) the four point function ofscalars near the Wilson-Fisher fixed point in $d=4-\epsilon$ as in\cite{Alday:2017zzv} and II) integrals for loop diagrams for massless $\phi^4$theory in position space in four dimensions. This suggests that a linearcombination of one expansion can be recast in terms of a linear combination ofthe other. As a by-product, we also derive the Mellin space representation forthe twist-2 higher spin conformal blocks. We also discuss the higher derivativecontact terms in the present scenario.

Relating diagrammatic expansion with conformal correlator expansion