Mathematica 7 represents another major achievement in Mathematica's long history of innovation in mathematics and algorithms. Building on the broad capabilities of ...
LucasL
(Built-in Mathematica Symbol) LucasL[n] gives the Lucas number L_n.LucasL[n, x] gives the Lucas polynomial L_n (x).
LinearRecurrence[ker, init, n] gives the sequence of length n obtained by iterating the linear recurrence with kernel ker starting with initial values ...
Composition[f_1, f_2, f_3, ...] represents a composition of the functions f_1, f_2, f_3, ....
RecurrenceTable[eqns, expr, {n, n_max}] generates a list of values of expr for successive n based on solving the recurrence equations eqns.RecurrenceTable[eqns, expr, nspec] ...
DifferenceRootReduce[expr, n] attempts to reduce expr to a single DifferenceRoot object as a function of n.
Nest
(Built-in Mathematica Symbol) Nest[f, expr, n] gives an expression with f applied n times to expr.
ExponentialGeneratingFunction[expr, n, x] gives the exponential generating function in x for the sequence whose n\[Null]^th term is given by the expression ...
GeneratingFunction[expr, n, x] gives the generating function in x for the sequence whose n\[Null]^th series coefficient is given by the expression ...
DiscreteRatio[f, i] gives the discrete ratio f(i + 1)/f(i).DiscreteRatio[f, {i, n}] gives the multiple discrete ratio.DiscreteRatio[f, {i, n, h}] gives the multiple discrete ...