RSolve - Qurak function reference

Solve recurrence equations.

Unabhängig überprüfbar: Eine Antwort für diese Funktion wird über einen anderen Weg neu hergeleitet und verglichen - die Werkbank und das Werkzeug verify tun dies automatisch, sodass eine falsche Antwort erkannt statt geglaubt wird. Verlauf →

Formen

RSolve[eqn, a[n], n]

RSolve[{eqn1, eqn2, …}, {a1[n], a2[n], …}, n]

RSolve[eqn, a[n1, n2, …], {n1, n2, …}]

Verifizierte BeispieleRSolve[a[n] == 2 a[n-1], a[n], n] → {{a[n] -> 2^(-1 + n)*C[1]}}RSolve[{a[n + 1] == 2 a[n], a[0] == 1}, a, n] → {{a -> Function[{n}, 2^n]}}RSolve[{a[n] == 2 a[n-1], a[2] == 5}, a[n], n] → {{a[n] -> 5*2^(-2 + n)}}RSolve[a[n] == 4 a[n-1] - 4 a[n-2], a[n], n] → {{a[n] -> 2^n*C[1] + 2^n*n*C[2]}}RSolve[{a[n] == a[n-1] + a[n-2], a[0] == 0, a[1] == 1}, a[n], n] → {{a[n] -> Fibonacci[n]}}RSolve[a[n] == a[n-1] + a[n-2], a[n], n] → {{a[n] -> C[1]*Fibonacci[n] + C[2]*LucasL[n]}}RSolve[{x[n + 1] == 4 x[n] (1 - x[n]), x[0] == 1/10}, x, n] → .* (regex*) {{x -> Function[{n}, (1 - Cos[2^n*ArcCos[4/5]])/2]}}RSolve[{x[n + 1] == 4 x[n] (1 - x[n])}, x, n] → {{x -> Function[{n}, 1/2 - Cos[2^n*C[1]]/2]}}

Auf Qurak ausführen Referenz durchsuchen

Themen

Calculus - Discrete Calculus »
Discrete Calculus - Difference Equations
Discrete Mathematics - Discrete Calculus »
Equation Solving - General
Integer Functions - Digit-Based Substitution System Functions
New In60 Mathematics And Algorithms - Some Functions with Major New Algorithms

Verwandt

RSolveValue AsymptoticRSolveValue RecurrenceTable RFixedPoints RStabilityConditions Sum ZTransform GeneratingFunction DifferenceRoot DSolve FindSequenceFunction FindGeneratingFunction