A holonomic sequence, also called a P-recursive sequence, is a sequence recurrence
equation
for all sufficiently large polynomials and are
not all zero (Stanley 1980, Zeilberger 1990).
Equivalently, the ordinary generating function holonomic
function . This equivalence allows differential
equations for generating functions and
recurrences with polynomial coefficients
to be translated into one another.
See also Coefficient ,
Differential Equation ,
Generating Function ,
Holonomic
Function ,
Recurrence Equation ,
Sequence
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References Stanley, R. P. "Differentiably Finite Power Series." Europ. J. Combin. 1 , 175-188, 1980. https://doi.org/10.1016/S0195-6698(80)80051-5 . Zeilberger,
D. "A Holonomic Systems Approach to Special Function Identities." J.
Comput. Appl. Math. 32 , 321-348, 1990.
Cite this as:
Weisstein, Eric W. "Holonomic Sequence."
From MathWorld https://mathworld.wolfram.com/HolonomicSequence.html
Subject classifications
satisfying a linear recurrence
equation
, where the 
are polynomials and are
not all zero (Stanley 1980, Zeilberger 1990).
is a holonomic
function. This equivalence allows differential
equations for generating functions and
recurrences with polynomial coefficients
to be translated into one another.
