A differential equation with six coefficients that sum to one is named for either Papperitz or this mathematician and generalizes the hypergeometric differential equation. This mathematician is the alphabetically latter namesake of the result that the Fourier transform of an L-one function vanishes at infinity. By introducing finer control of mesh size, Thomas Stieltjes (15[1])improved (15[1])an operation (15[1])named for (15[1])this (15[2])mathematician (15[2]10[1])that is equivalent (15[2]-5[1])to the (-5[1])Darboux (15[1])definition, (15[2]-5[1])which (15[1])replaces (15[2])a requirement (15[2]-5[2])of the convergence of all tagged partitions with (*) upper and lower sums. (10[2])This mathematician (10[1]-5[1])co-names a lemma with Henri Lebesgue, (10[3])who also generalized an object named for this mathematician (10[1])that might be approximated with (10[2])the midpoint or trapezoid (10[4])rules. (10[6]-5[1])For 10 (10[1])points, (10[4])name (10[1])this German mathematician (10[1])whose (10[1])namesake (10[1])“sums” (10[3])are used (10[1])to (10[1])define (10[1])an integral. (10[2])■END■ (10[5]0[1])