Identities of Rothe-Abel- Schläfli-Hurwitz-type

Chromatic Statistics for Triangulations and Fuß–Catalan Complexes

“…This is a special case of an identity commonly attributed to Rothe [12] (to be precise, it is the case α → β 1 s, β → −1, γ → β 2 s + β 1 + β 2 , n → γ − β 1 − β 2 of [9, Eq. (4)]; see [16] for historical comments and more on this kind of identities, although, for some reason, it misses [3]), which establishes the induction step in this case. Suppose now that Theorem 2.2 holds for all (suitable) sequences β 0 , β 1 , β 2 , .…”

On Jensen's and related combinatorial identities

“…Note that the corresponding multinomial coefficient generalization of Rothe's identity was already obtained by Raney [22] (for a special case) and Mohanty [18]. The reader is referred to Strehl [28] for a historical note on Raney-Mohanty's identity.…”

The Pfaff/Cauchy derivative identities and Hurwitz type extensions

“…This is due to Jensen [17] when h = 1, and if h = 0 it reduces to (3.4). Some good references for Abel-Rothe type identities are [10,11,39]. This surprising formula has a number of uses in mathematics, among them the derivation of Abel-Rothe type identities.…”