Recurrence and Sum Functions

Mathematica has a wide coverage of named functions defined by sums and recurrence relations. Often using original algorithms developed at Wolfram Research, Mathematica supports highly efficient exact evaluation even for results involving millions of digits.

ReferenceReference

Fibonacci, LucasL Fibonacci and Lucas numbers and polynomials

BernoulliB Bernoulli numbers and polynomials

NorlundB Nörlund polynomials and generalized Bernoulli polynomials

EulerE Euler numbers and polynomials

StirlingS1, StirlingS2 Stirling numbers

HarmonicNumber harmonic numbers

PolyGamma polygamma functions

Zeta ▪ LerchPhi ▪ PolyLog

Factorial (!) ▪ Factorial2 (!!) ▪ FactorialPower ▪ Binomial ▪ CatalanNumber ▪ BellB

RecurrenceTable create tables of values from recurrences and functional equations

LinearRecurrence ▪ FindLinearRecurrence

RSolve solve general recurrence relations

Sum compute general finite and infinite sums

MatrixPower ▪ GeneratingFunction ▪ SeriesCoefficient

DifferenceRoot symbolic representation of solutions to linear difference equations

FindSequenceFunction find functional forms from sequences

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