[eigen] Raising double to integer powers

I have a simple question that I have spent ages trying to work around over the years and still haven't found a satisfactory solution. I have a single double value, and without any allocation, I need to generate an Eigen _expression_ that allows me to take a double to an array of integers. In my case, 25% of my code's execution time is spent working on this problem, and I think I should be able to get that contribution back to closer to zero. Initially I asked the question here: https://stackoverflow.com/questions/25354205/how-to-raise-double-to-array-powers-in-eigen

This code doesn't compile (e.g., on godbolt):

#include <Eigen/Dense>

int main(){
    auto c = Eigen::ArrayXi::LinSpaced(11, 0, 10);
    auto r = Eigen::pow(3.7, c);
}

but if I switch the ArrayXi for ArrayXd it compiles (because the scalar types match), but that is not what I want.  

Really, what I need is to call my own implementation of pow(double, int), because it is MUCH faster than pow(double, double).  

In the end, I would like some guidance on how I can craft an Eigen _expression_ for this use case that will not introduce any intermediate allocation.  

Thanks,
Ian