  We propose a series representation for the Virasoro fusion and modular
kernels at any irrational central charge. Two distinct, yet closely related
formulas are needed for the cases $c\in \mathbb C \backslash (-\infty,1]$ and
$c <1$. We also conjecture that the formulas have a well-defined limit as the
central charge approaches rational values. Our proposal for $c <1$ agrees
numerically with the fusion transformation of the four-point spherical
conformal blocks, whereas our proposal for $c\in \mathbb C \backslash
(-\infty,1]$ agrees numerically with Ponsot and Teschner's integral formula for
the fusion kernel. The case of the modular kernel is studied as a special case
of the fusion kernel.
