caa a22 4500 463178335 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s11139-006-0246-0 doi (NATIONALLICENCE)springer-10.1007/s11139-006-0246-0 Johnson Warren Department of Mathematics, Bates College, 04240, Lewiston, Maine aut The Pfaff/Cauchy derivative identities and Hurwitz type extensions [Elektronische Daten] [Warren Johnson] More than 200 years ago, Pfaff found two generalizations of Leibniz's rule for the nth derivative of a product of two functions. Thirty years later Cauchy found two similar identities, one equivalent to one of Pfaff's and the other new. We give simple proofs of these little-known identities and some further history. We also give applications to Abel-Rothe type binomial identities, Lagrange's series, and Laguerre and Jacobi polynomials. Most importantly, we give extensions that are related to the Pfaff/Cauchy theorems as Hurwitz's generalized binomial theorems are to the Abel-Rothe identities. We apply these extensions to Laguerre and Jacobi polynomials as well. Springer Science + Business Media, LLC, 2006 Derivative identities nationallicence Abel-Rothe identities nationallicence Hurwitz type identities nationallicence Lagrange's series nationallicence Laguerre and Jacobi polynomials nationallicence The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 167-201 1382-4090 13:1-3<167 2007 13 11139 https://doi.org/10.1007/s11139-006-0246-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-0246-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Johnson Warren Department of Mathematics, Bates College, 04240, Lewiston, Maine aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 167-201 1382-4090 13:1-3<167 2007 13 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer