Convergents - MathStudio Manual

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

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A

AlternatingSeries(n, [terms])

Angle(A, B)

Animate(variable, start, end, [step], [value], [fps])

Apart(f(x), x)

Append(expression1, expression2)

B

BarPlot(list1, frequency1, ...)

Bernoulli(n, [z])

BesselI(v, z)

BesselJ(v, z)

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Button(name, [list], [value])

G

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)

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http(url, [filter])

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J

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json(data, [filter])

JuliaPlot(expression, ...)

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M

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MultiPlot(plot1, plot2, ...)

MultiPlot3D(expression, ...)

N

nCr(n, r)

NIntegrate(f(x), x, a, b)

NormalCDF(lower, upper, [mu], [sigma])

NormalPDF(x, mu, sigma)

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nRoot(z, n, [mode])

Q

QuadraticFit([x], y)

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QuarticFitModel([x], y)

QuarticFitPlot([x], y)

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R

Random(min, max, [size1], [size2])

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)

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])