Mariusz Iwaniuk

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These are questions asked by Mariusz Iwaniuk

Hi!

How to calculate  a value in MAPLE:

My code:

evalf(eval(diff(n*Zeta(n, 3), n), n = 3)); give me:

#-0.3740436824 + 3.*eval(diff(Zeta(n, 3), n), {n = 3}) ,it should be only:-0.3740436824

OR:

fdiff(n*Zeta(n, 3), [n], n = 3);

#fdiff(n -> n*Zeta(n, 3), [1], [3]) ???

It's a Bug  or (As Designed / Not a Bug) ?

Thanks in advance.

 

Mathematica code:

D[n*Derivative[n][Zeta][3], n] /. n -> 3 // N;

(* -0.374044*)

 

 

Hi, fairly simple question,

I solve a simple equation:

solve(x^x = 4, allsolutions, explicit);

#(2*(I*Pi*_Z7+ln(2)))/LambertW(_Z9, 2*ln(2)+(2*I)*Pi*_Z7)

Maple  gave me solution with prefix _Z for integer values, but why  _Z9 must be exactly equal  Zero  to be correct ?.

If _Z9 is integer it can also take other values than zero ?

Thanks in advance.



More information see attached file:

Download Allsolution.mw

 

Hello

The problem is translate Mathematica code to Maple to find  numerical solution using int(numeric).

I have a more complicated example and here I gives a very simplified version.

I use  successive approximations to solve integral-equation with symbolic int it's easy to do,but with numeric int  I'm failed

MMA code:

func[x_, 0] := x
ifunc[0][x_] := x
func[x_?NumericQ, n_Integer] := x + NIntegrate[(x - y)*ifunc[n - 1][y], {y, 0, x}]
ifunc[j_Integer] := ifunc[j] = Interpolation[Table[{x, func[x, j]}, {x, -3, 3, 0.2}]]

Plot[{Sinh[x], ifunc[n][x] /. n -> 4}, {x, -3, 3}]


My first attempt to translate:

ifunc := proc (n, x) options operator, arrow; x end proc;

ifunc(0, x) := x;

func(x, 0) := x;

func := proc (x, n) x+int((x-t)*ifunc(n-1, t), t = 0 .. x, numeric) end proc;

T := proc (j) option remember;

Interpolation:-Interpolate([seq(x, x = -2 .. 2, .1)], [seq(func(x, j), x = -2 .. 2, .1)], method = cubic)

end proc;

plot([sinh(x), (T(4))(x)], x = -2 .. 2);

See attached file for more info.

Thanks.

test_numeric_volterra.mw

EDITED :----------------------------------------------------------

Third attempt:

func(x, 0) := x;

(ifunc(0))(x) := x:

func := proc (x, n) option remember; x+int((x-t)*(ifunc(n-1))(t), t = 0 .. x, numeric) end proc;

ifunc := proc (j) local f; option remember;

ifunc(0) := proc (t) options operator, arrow; t end proc;

f := proc (t) options operator, arrow;

CurveFitting:-Spline([seq(x, x = -3 .. 3, .1)], [seq(func(x, j), x = -3 .. 3, .1)], x, degree = 1) end proc end proc;

n := 4; plot([sinh(x), (ifunc(n))(x)], x = -3 .. 3)# for n=4 diverge !!!

Hello

I want to compute integral with Maple,but returns unevaluated for me.

int((-5*ln(x)^4*Pi^4-20*ln(x)^2*Pi^4-8*Pi^4+120*MeijerG([[0, 0], [1, 1, 1]], [[0, 0, 0, 0, 0], []], x^Pi))/(120*Pi^4*(-1+x)^2), x = 4/10 .. 6/10, numeric);

# ???

Thanks.

Hello

I'd like Maple to return ln(abs(x)) for int(1/x,x) instead of ln(x).

I tried convert MMA code,but I failed.

realIntegrate[f_, x_Symbol] := 
 Simplify[Integrate[f, x] /. Log[expr_] :> Log[Abs[expr]], 
  x \[Element] Reals]; Unprotect[Integrate]; 
Integrate[f_, x_Symbol] /; ! TrueQ[$flag] := 
 Block[{$flag = True}, realIntegrate[f, x]]; Protect[Integrate];

My maple code works only for very simple cases.

REALINT := proc (f, x)

if typematch(int(f, x), ln(y::anything), 's') then

`assuming`([simplify(ln(abs(rhs(s[1]))))], [x in real])

else int(f, x)

end if

end proc;

REALINT(1/x, x);

#ln(abs(x))

REALINT(1/(x+1), x);

#ln(abs(x+1))

REALINT(1/x+1, x);

#x+ln(x) dosen't work.

 

Thanks.

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