Exponential divided difference
= Exponential divided difference
{title2=$D_t(\beta,\gamma)=\int_0^te^{(t-x)\gamma+x\beta}\,dx$}
The displayed integral is $(e^{t\beta}-e^{t\gamma})/(\beta-\gamma)$ for distinct exponents and $te^{t\gamma}$ when they coincide. The latter is the continuous limit, so a zero denominator is a removable singularity. This quantity appears in <variation-of-constants formula> estimates of <matrix> evolution and avoids omitting an equal-exponent case.