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On a Functional Differential Equation of Determinantal Type
Author(s) -
Braden H. W.,
ByattSmith J. G. B.
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398005542
Subject(s) - mathematics , functional equation , mathematics subject classification , type (biology) , differential equation , subject (documents) , pure mathematics , function (biology) , combinatorics , mathematical analysis , mathematical physics , algebra over a field , ecology , evolutionary biology , library science , computer science , biology
We solve the functional equations|1 1 1f ( x )f ( y )f ( z )f ′ ( x )f ′ ( y )f ′ ( z )| = 0 , |1 1 1f ( x )g ( y )h ( z )f ′ ( x )g ′ ( y )h ′ ( z )| = 0 ,for suitable functions f , g and h subject to x + y + z = 0. These equations essentially characterise the Weierstrass p‐function and its degenerations. 1991 Mathematics Subject Classification 39B22, 30D05, 33E05.