sum of i.i.d. exponentially distributed random variables with geometrically distributed number of summands

It is well know that the sum of independent squared normally
distributed random variables (rv's) has a chi-square distribution. A
sum of exponentially distributed rv's is gamma distributed.

So can anyone tell me if there is an explicit distribution according to
which a sum of exponentially distributed rv's with a geometrically
distributed number of summands is distributed?

Many thanks for help, tips, references, ...
pkg

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