MathStudio MathStudio Express

Convergents(n, [mode=0], [terms])

n
Real number or [numerator, denominator] of a real number or [continued fraction] of a real number

[mode=0]
mode = 0 returns the maximum number of convergents MathStudio can calculate. The result is displayed in a matrix with the top row = numerator and the bottom row = denominator of the convergent.
mode = 1 returns the same as above, but the result is displayed as a fraction (less accurate compared to above...)
mode = -1 returns only the largest convergent it can find with both numerator and denominator < 15 digits

[terms]
Number of convergents to return (default = maximum, and limited by machine precision)

Description

The Convergent of a given number or a given continued fraction is the rational number obtained by keeping only a limited number of terms in the continued fraction (or the continued fraction of the number).

Examples

Convergents([3, 7, 15, 1, 292, 1, 1])
Convergents([3, 7, 15, 1, 292, 1, 1], 1)
Convergents(2/@pi, -1)
Convergents(@pi, 1, 10)
Convergents([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], -2)

References

http://mathworld.wolfram.com/Convergent.html

Related Functions

AlternatingSeries, cFrac
Using MathStudio
The Basics
1. Introduction
2. Trigonometric Functions
3. Special Values
4. Lists
5. Matrices
6. Algebra
7. Calculus
8. Fourier Analysis
9. Units
10. Base Conversions
11. Regression Analysis
12. Natural Language
13. Constants
14. Dynamic Variables
Operators
1. Basic Operators
2. Double Power Operator
3. Comparison Operators
4. Logical Operators
5. Compound Assignment Operators
6. Type Comparison Operators
7. Size Operator
8. Range Operator
9. Transformation Operator
10. Index Operator
11. Union Operator
12. Intersection Operator
13. Difference Operator
14. Double Modulo Operator
15. Matrix Operator
16. Matrix Size Operator
17. Angle Operator
18. Choose Operator
19. String Concatenation Operator
20. Conditional Operator
21. Append Operator
22. Element Operator
Graphing
1. 2D Graphing
2. Plot Styles
3. Min, Max and Zero Values
4. 3D Graphing
5. Multiple Plots
6. Color Names
7. Time Graphing
Scripting Language
Variables
1. Creating Variables
2. Unicode Characters
3. Variable Functions
4. Strings
5. Wildcards
Scripts
1. Creating Scripts
2. Semicolons
3. Comments
4. Variable Controls
5. Conditional Statements
6. For-In Loops
7. While Loops
8. Timing
9. Objects
10. Working with JSON
Functions
A
abs(z)
AiryAi(z)
AiryBi(z)
AlternatingSeries(n, [terms])
Angle(A, B)
Animate(variable, start, end, [step], [value], [fps])
Apart(f(x), x)
Append(expression1, expression2)
Arg(z)
B
BarPlot(list1, list2, ...)
Bernoulli(n, [z])
BesselI(v, z)
BesselJ(v, z)
BesselK(v, z)
BesselY(v, z)
Beta(m, n)
Binomial(n, r)
BinomialCDF(n, p, x)
BinomialPDF(n, p, x)
BodePlot(function, variable, minimum, maximum, mode)
BoxPlot(x, [y], [x2], [y2], ...)
Button(name, [list], [value])
C
Call(function, parameter1, parameter2, ...)
Caps(string, index, [mode])
Catalan(n)
Ceil(z)
cFrac(n, [terms])
Char(x)
ChebyshevT(n, z)
ChebyshevU(n, z)
CheckBox(variable, [value])
Chi(z)
ChiSquareCDF(lower, upper, df)
ChiSquarePDF(x, df)
Cholesky(A)
Choose(test1, value1, test2, value2, ...)
Ci(z)
Clear(variable, ...)
clip(x, [min], [max])
Coefficient(f(x), x, degree)
coFactor(matrix, i, j)
Command(setting)
Conj(z)
ContourPlot(expression, ...)
Convergents(n, [mode=0], [terms])
Cross(A, B)
CubicFit([x], y)
CubicFitModel([x], y)
CubicFitPlot([x], y)
Curl(vector, [varlist], [mode])
CylindricalPlot3D(expression, ...)
D
D(f(x), x, [n])
Date(letter)
Dawson(z)
Degree(expression)
DEGtoDMS(angle, [digits])
Delete(expression, position, [length])
Denominator(expression)
Det(A)
Diff(f(x), x)
DiGamma(z)
DiLog(z)
Dirichlet_Eta(z)
Dirichlet_Lambda(z)
Divergence([varlist], vector, [mode])
Divisors(n)
DivisorSigma(n)
Dot(A, B)
DSolve(equation, dependent(independent), values, mode=1)
Duf(function, [varlist], [point], [direction])
dynamic(name, value)
E
Ei(z)
Eigenvalues(A)
Eigenvectors(A)
Else If(condition)
Erf(z)
Erfc(z)
Error(string)
Euler(n, [z])
Eulerian(n, k)
Eval(function, variable, value)
Exp(z)
Expand(expression)
ExpConvert(expression)
ExpFit([x], y)
ExpFitModel([x], y)
ExpFitPlot([x], y)
ExponentialFit([x], y)
ExponentialFitModel([x], y)
ExponentialFitPlot([x], y)
Extract(expression, position, [length])
F
Factor(expression)
Factorial(n)
Fcdf(lower, upperbound, numerator, denominator)
fDiff(f(x,y,z,..), (x,y,z,...))
Fibonacci(n, [z])
Finance(PV, FV, Pmt, i, n, [mode=0])
FindFit(function, variable, [x], y)
FindFitModel(function, variable, [x], y)
FindFitPlot(function, variable, [x], y)
Flatten(matrix)
Floor(z)
FourierCos(f(x), x, w)
FourierExpSeries(f(x), x, n)
FourierSeries(f(x), x, [n], [mode])
FourierSin(f(x), x, w)
FourierTrigSeries(f(x), x, n)
fPart(z)
Fpdf(x, d1, d2)
FractalPlot(expression, ...)
FresnelCos(z)
FresnelSin(z)
FullRectSineWave(x, [T])
Function(function, parameter1, parameter2, ...)
G
Gamma(z)
GCD(n1, n2)
GegenbauerC(n, a, z)
GeoCDF(p, x)
GeoPDF(p, x)
Gradient(function, [varlist], [mode])
Gudermannian(z)
H
HalfRectSineWave(x, [T])
HankelH1(v, z)
HankelH2(v, z)
Harmonic(z)
Heaviside(x)
HermiteH(n, z)
Hessian(function, [varlist], [mode])
HRStoHMS(hours, [digits])
http(url, [filter])
Hypergeom_2F1(a, b, c, z, [mode])
I
Identity(n)
iDiff(f(x,y,z,..), dependant_variables, independant_variables)
If(condition)
iLaplace(F(s), s)
Im(z)
ImagePlot(data)
ImaginaryPart(expression)
ImplicitPlot(expression, ...)
Include(filename)
Insert(expression, item, position)
Integrate(f(x), x, [a], [b])
Inverse(A)
InverseNormal(p, [mu], [sigma])
invGudermannian(z)
iPart(z)
IsList(expression)
IsMatrix(expression)
IsNumber(expression)
IsPoly(expression, variable)
IsPrime(n)
J
Jacobian(function, [varlist], [point])
json(data, [filter])
JuliaPlot(expression, ...)
K
KelvinBei(v, z)
KelvinBer(v, z)
KelvinKei(v, z)
KelvinKer(v, z)
L
LaguerreL(n, z)
LambertW(z)
Laplace(f(t), t)
Laplacian(function, [varlist], [mode])
LCM(n1, n2)
Left(expression)
LegendreP(n, z)
LegendreQ(n, z)
Length(expression)
Li(x)
Limit(function, variable, point, [direction])
LinearFit([x], y)
LinearFitModel([x], y)
LinearFitPlot([x], y)
List(length)
ListMap(list, name, [value])
ListPlot(x, [y], [x2], [y2])
ListPlot3D(x, y, z, [x2], [y2], [z2], ...)
Ln(z)
LnFit([x], y)
LnFitModel([x], y)
LnFitPlot([x], y)
LnGamma(z)
local(name, value)
Log([n], z)
LogisticFit([x], y)
LogisticFitModel([x], y)
LogisticFitPlot([x], y)
Lucas(n, [z])
M
Matrix(rows, [columns])
MatrixLU(matrix, [mode])
MatrixMap(matrix, name, [value])
MatrixQR(A)
MatrixSVD(A)
Max(number, ...)
Mean(list)
MedianFit([x], y)
MedianFitModel([x], y)
MedianFitPlot([x], y)
Message(string)
Min(list)
Mod(m, n)
Multinomial(nList)
MultiPlot(plot1, plot2, ...)
MultiPlot3D(expression, ...)
N
nCr(n, r)
NIntegrate(f(x), x, a, b)
Norm(z)
NormalCDF(lower, upper, [mu], [sigma])
NormalPDF(x, mu, sigma)
nPr(n, r)
nPrimes(n)
nRoot(z, n, [mode])
P
ParametricPlot(expression, ...)
ParametricPlot3D(expression, ...)
Part(expression, n)
pDiff(f(x,y,z,..), dependent_variables, dependent_equations, independent_variables)
Pi_Digits(n)
Plot(expression, ...)
Plot3D(expression, ...)
Pochhammer(n, k)
PoissonCDF(mu, x)
PoissonPDF(mu, x)
PolarPlot(expression, ...)
PolyDivide(f(z), g(z))
PolyFit(pList, var)
PolyGamma(n, z)
PolyGCD(polynomial1, polynomial2)
PolyLCM(polynomial1, polynomial2, [mode=1])
PolyLog(n, z)
PowerExpand(expression)
PowerFit([x], y)
PowerFitModel([x], y)
PowerFitPlot([x], y)
Prime(n)
Primorial(n)
Product(f(n), n, start, end)
Psi(z)
Q
QuadraticFit([x], y)
QuadraticFitModel([x], y)
QuadraticFitPlot([x], y)
QuarticFit([x], y)
QuarticFitModel([x], y)
QuarticFitPlot([x], y)
Quotient(f(x), g(x))
R
Random(min, max, [size1], [size2])
Re(z)
RealPart(expression)
Remainder(f(x), g(x))
Replace(expression, old, new)
Reshape(matrix)
Return(expression)
Reverse(list)
Right(expression)
RK4(function, t, y, a, b, y0, N=10)
RK45(function, t, y, a, b, y0, Tol=10E-5, hmax=0.25, hmin=10E-6, N=20)
Round(number, digits)
RowReduce(A)
S
SawToothWave(x, [T])
Sequence(f(x), x, start, end, [step], [start term], [number of terms])
Series(f(z), z, n)
Shi(z)
Si(z)
Sign(z)
SimplifyFunction(expression)
SimplifyPoly(f(x)/g(x), [variable])
sin(z)
SinFit([x], y)
SinFitModel([x], y)
SinFitPlot([x], y)
Size(list)
Slider(variable, start, end, [step], [initial value])
Solve(f(x), x, [guess])
SolveSystem(equations, [variables], [guesses])
Sort(list)
SphericalPlot3D(expression, ...)
Sqrt(z)
SquareWave(x, [T])
StaircaseWave(x, [T])
StandardDeviation(list)
String(expression1, expression2, ...)
StudentTCDF(x, df)
StudentTPDF(x, df)
Sum(f(n), n, start, end)
SurfaceNormal(function, [varlist], [point])
T
Together(expression)
Trace(variable)
Transpose(A)
TriangleWave(x, [T])
TrigConvert(expression)
TrigExpand(expression)
TrigReduce(expression)
V
Variables(expression)
Variance(list)
VectorPlot(list, ...)
VectorPlot3D(list, ...)
W
While(condition)
Z
Zeta(z, [a])