Buenisimo

MathStudio Manual

Abs(z)
Returns the complex modulus (or magnitude) of a complex number.
abs(-3)

abs(-x)

abs(\im)

AiryAi(z)
Returns the Airy function Ai(z).
AiryAi(2)

AiryAi(3-\im)

AiryAi(\pi/2)

AiryAi(-9)

Plot(AiryAi(x),x=[-10,1],numbers=0)

Page 1/188

MathStudio Manual

AiryBi(z)
Returns the Airy function Bi(z).
AiryBi(0)

AiryBi(10)

AiryBi(1+\im)Plot(AiryBi(x),x=[-10,1],numbers=0)

AlternatingSeries(n, [terms])

Page 2/188

MathStudio Manual
This function approximates the given real number in an alternating series.
The result is returned in a matrix with the top row = numerator and the bottom row
= denominator of the different terms.
Note the alternating sign in the numerator!
AlternatingSeries(\pi,7)AlternatingSeries(ln(2),10)

AlternatingSeries(sqrt(2),10)

AlternatingSeries(-3.23)

AlternatingSeries(123456789/987654321)

AlternatingSeries(.666)

AlternatingSeries(.12121212)

Page 3/188

MathStudio Manual

AlternatingSeries(.36363)

Angle(A, B)
Returns the angle between the two vectors A and B.
Angle([a@1,b@1,c@1],[a@2,b@2,c@2])

Angle([1,2,3],[4,5,6])

Animate(variable, start, end,[step])
This function creates an animated entry. The variable is initialized to the start
value and at each frame is incremented by step and the entry is reevaluated
creating animation.
When the variable is greater than the value end it is set back to start.
Animate(n,1,100) ImagePlot(Random(0,1,n,n))

Page 4/188

MathStudio Manual

Apart(f(x), x)
Performs partial fraction decomposition onthe polynomial function.
Apart performs the opposite operation of Together.
Apart((a+b)/(a*b),a)

Apart((a+b)/(a*b),b)

Apart((x^2+x+1)/((x-2)(x^2+3)))

Apart((2x^2+3x+5)/(x^2+2x+1))

Append(expression1, expression2)
Page 5/188

MathStudio Manual
Appends one expression to end of another expression.
Append([1,2,3],4)

Append([1,2,3],[4,5,6])

Append(ab,c)

Append(a,1)Arg(z)
Returns the argument (or phase) of a complex number.
The value is dependent on the angle setting which can be radians or degrees.
You can manually set the angle mode per entry by using the keyword radians or
degrees.
radians arg(2+2\im)

degrees arg(2+2\im)

Bernoulli(n, [z])
Returns the nth Bernoulli number n.
If z is given, returns the nth Bernoulli polynomial of z.
Bernoulli(3,a)Page 6/188

MathStudio Manual

Bernoulli(n,1/2)

Bernoulli(n,3)

Bernoulli(n,-z)

Bernoulli(n,5)

Bernoulli(n,-5)

Bernoulli(3,5)

Bernoulli(4,5)

BesselI(v, z)
Returns the Modified Bessel function of the first kind.
BesselI(0,15\im)

Page 7/188

MathStudio Manual
BesselI(1,14.99)
BesselI(-1,15)

BesselI(1,30)BesselI(1/2,x)+BesselK(1/2,x)+BesselY(1/2,x)+BesselJ(1/2,x)

BesselI(3,x+1)

BesselI(3,x)

Plot([BesselI(0,x),BesselI(1,x),BesselI(2,x),BesselI(3,x)],colors=[red,blue,gree
n,magenta])

BesselJ(v, z)
Returns the Bessel function of the first kind.

Page 8/188

MathStudio Manual
BesselJ(0,1)

BesselJ(1,1)

BesselJ(2,1-\im)

BesselJ(2,x)

BesselJ(3,-x)

BesselJ(5/2,x)Plot([BesselJ(0,x),BesselJ(1,x),BesselJ(2,x),BesselJ(3,x)])

Plot3D(BesselJ(1,sqrt(x^2+y^2)),x=[-10,10],y=[-10,10],z=[-2,2])

Page 9/188

MathStudio Manual

Diff(BesselJ(2,3z),z)

BesselK(v, z)
Returns the Modified Bessel function of the second kind.
BesselK(0,0)

BesselK(0,2)

BesselK(2.3,1.5)

BesselK(3/2,x)

BesselK(3/2,-z)

Page 10/188

MathStudio Manual

BesselK(1,2+3\im)Plot([BesselK(0,x),BesselK(1,x),BesselK(2,x),BesselK(3,x)],x=[-1,5])

BesselY(v, z)
Returns the Bessel function of the second kind.
BesselY(0,1)

BesselY(2,x)

BesselY(1.23,45.67)

BesselY(3/2,x)

Page 11/188

MathStudio Manual

Plot([BesselY(0,x),BesselY(1,x),BesselY(2,x),BesselY(3,x)],x=[-1,6],y=[-2.5,2.
5])

Beta(m, n)
Calculates the Beta function of m, n both real or complex variables.
Beta(m,n)

Beta(2n,n)...