TY - JOUR
T1 - Lie theory and difference equations. I
AU - Miller, Willard
PY - 1969/11
Y1 - 1969/11
N2 - A factorization method is constructed for sequences of second-order linear difference equations in analogy with the factorization method for differential equations. Six factorization types are established and recursion relations are obtained for various classes of special functions, among which are the hypergeometric functions and their limits, and the classical polynomials of a discrete variable: Tchebycheff, Krawtchouk, Charlier, Meixner, and Hahn. It is shown that the factorization method is a disguised form of Lie algebra representation theory.
AB - A factorization method is constructed for sequences of second-order linear difference equations in analogy with the factorization method for differential equations. Six factorization types are established and recursion relations are obtained for various classes of special functions, among which are the hypergeometric functions and their limits, and the classical polynomials of a discrete variable: Tchebycheff, Krawtchouk, Charlier, Meixner, and Hahn. It is shown that the factorization method is a disguised form of Lie algebra representation theory.
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U2 - 10.1016/0022-247X(69)90037-7
DO - 10.1016/0022-247X(69)90037-7
M3 - Article
AN - SCOPUS:18644384272
SN - 0022-247X
VL - 28
SP - 383
EP - 399
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -