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

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  ▪  Fibonorial  ▪  AlternatingFactorial

RecurrenceTable — create tables of values from recurrences and functional equations

LinearRecurrence  ▪  FindLinearRecurrence  ▪  FindRepeat  ▪  FindTransientRepeat

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

RFixedPoints — fixed points for a system of difference equations

RStabilityConditions — stability conditions for a system of difference equations