Angelo Melino

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7 years, 130 days

MaplePrimes Activity


These are questions asked by Angelo Melino

I came across what looks to me like an error in Maple 2023.  If it stands alone, Maple evaluates z^0/0! to 1, but inside the sum command it appears to evaluate the same expression to 0.

Download Weird_sum_behaviour.mw

I was surprised to learn that implicitplot doesn't recognize the constant Pi.  I attach a simple example to illustrate.

restart

with(plots)

f := x-y-Pi

x-y-Pi

(1)

implicitplot(f)

Error, (in plots/implicitplot) found 3 variables that the expression depends on ({Pi, x, y}), but expected only 2

 

evalf(Pi)

3.141592654

(2)

g := x-y-3.14

x-y-3.14

(3)

implicitplot(g)

 

NULL

Download implicitplot_error.mw

I have an example where I try to calculate an infinite sum (G&R1.641.1)  in Maple 2022 (or 2021).  I get a different numerical result when I evaluate the sum if I express the coefficients c(m) in the sum using Maple's doublefactorial function for m!! (c1(m)) or the equivalent expression involving the factorial function (c2(m)).  Only the latter gives the correct value for the sum.  This happens even though Maple gives the same numerical value for the coefficients c1(m) and c2(m).  What's going on?? Please see the attached spreadsheet.

Download doublefactorial_test.mw

I'm using MAPLE 2019 and I'm sometimes surprised by its behaviour.  For example, I appear to have an example where it evaluates the integral of each of two terms but not their sum...  What's going on?  Please see the attached.

restart

g0 := exp(r*cos(theta))/Pi

exp(r*cos(theta))/Pi

(1)

G0 := `assuming`([int(g0, theta = 0 .. Pi)], [r > 0])

BesselI(0, r)

(2)

g1 := exp(r*cos(theta))*cos(theta)/Pi

exp(r*cos(theta))*cos(theta)/Pi

(3)

G1 := `assuming`([int(g1, theta = 0 .. Pi)], [r > 0])

BesselI(1, r)

(4)

g := g0+g1

exp(r*cos(theta))/Pi+exp(r*cos(theta))*cos(theta)/Pi

(5)

G := `assuming`([int(g, theta = 0 .. Pi)], [r > 0])

int(exp(r*cos(theta))/Pi+exp(r*cos(theta))*cos(theta)/Pi, theta = 0 .. Pi)

(6)

``


 

Download Maplesumint.mw

I compared the numerical value of an integral expression in Gradshteyn and Rhyzhik (8.431.5) for the BesselI(v,z) function to the BesselI(v,z) function in Maple 2019.2 and got different answers.  The GR expression is the difference of two integrals and it looks like Maple only evaluates the first integral, which is correct only if the order v is an integer.  Please see the attached.

BesselI.mw

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