Heinrich August Rothe (1773–1842) was a German mathematician, a professor of mathematics at Erlangen.
[1][2] Rothe was born in 1773 in Dresden, and in 1793 became a docent at the University of Leipzig.
[3][4] The Rothe–Hagen identity, a summation formula for binomial coefficients, appeared in Rothe's 1793 thesis.
[5] The same thesis also included a formula for computing the Taylor series of an inverse function from the Taylor series for the function itself, related to the Lagrange inversion theorem.
He found the recurrence relation for counting these permutations, which also counts the number of Young tableaux, and which has as its solution the telephone numbers Rothe was also the first to formulate the q-binomial theorem, a q-analog of the binomial theorem, in an 1811 publication.