Mariusz Iwaniuk

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4 years, 39 days

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These are replies submitted by Mariusz Iwaniuk

@Mohamed19 


 

restart

J := proc (alpha, u) options operator, arrow; simplify(sum(GAMMA(alpha+1)*(-1)^m*((1/2)*u)^(2*m)/(factorial(m)*GAMMA(alpha+m+1)), m = 0 .. infinity)) end proc

proc (alpha, u) options operator, arrow; simplify(sum(GAMMA(alpha+1)*(-1)^m*((1/2)*u)^(2*m)/(factorial(m)*GAMMA(alpha+m+1)), m = 0 .. infinity)) end proc

(1)

J(alpha, u)

BesselJ(alpha, u)*GAMMA(alpha+1)*2^alpha*u^(-alpha)

(2)

NULL

evalf(eval(diff(J(alpha, u), u), [u = 1, alpha = 1]))

-.2298069698

(3)

evalf(eval(-u*J(alpha+1, u)/(2*(alpha+1)), [u = 1, alpha = 1]))

-.2298069698

(4)

Diff('J(alpha, u)', `$`(u, n)) = sum(simplify(diff(GAMMA(alpha+1)*(-1)^m*((1/2)*u)^(2*m)/(factorial(m)*GAMMA(alpha+m+1)), `$`(u, n))), m = 0 .. infinity)

Diff(J(alpha, u), `$`(u, n)) = hypergeom([1/2, 1], [alpha+1, 1-(1/2)*n, -(1/2)*n+1/2], -(1/4)*u^2)/(u^n*GAMMA(-n+1))

(5)

eval(eval(rhs(Diff(J(alpha, u), `$`(u, n)) = hypergeom([1/2, 1], [alpha+1, 1-(1/2)*n, -(1/2)*n+1/2], -(1/4)*u^2)/(u^n*GAMMA(-n+1))), [alpha = 1, u = 1]), n = .999999999)

-.2298069689

(6)

eval(eval(rhs(Diff(J(alpha, u), `$`(u, n)) = hypergeom([1/2, 1], [alpha+1, 1-(1/2)*n, -(1/2)*n+1/2], -(1/4)*u^2)/(u^n*GAMMA(-n+1))), [alpha = 1, u = 1]), n = 1.000000001)

-.2298069709

(7)

limit(eval(rhs(Diff(J(alpha, u), `$`(u, n)) = hypergeom([1/2, 1], [alpha+1, 1-(1/2)*n, -(1/2)*n+1/2], -(1/4)*u^2)/(u^n*GAMMA(-n+1))), [alpha = 1, u = 1]), n = 1)

limit(hypergeom([1/2, 1], [2, 1-(1/2)*n, -(1/2)*n+1/2], -1/4)/GAMMA(-n+1), n = 1)

(8)

plot(hypergeom([1/2, 1], [2, 1-(1/2)*n, -(1/2)*n+1/2], -1/4)/GAMMA(-n+1), n = 1/2 .. 3/2)

 

``


 

Download BesselI_n-th_derivative_2.mw

@NickH 

Try this.

@Oliveira 

Try add evalf command:

evalf(eval(-Gradient(uval(r, t), 'cylindrical'[r, theta, z]), [r = 2, t = 4]));

 

I don't know why there is a problem here,but you use workaround:

eval(solve({-1 < b, a < -1, b < 0, -z < a}), z = infinity);

#{-1 < b, a < -1, b < 0, -a < infinity}

It works for me (see the attached file).

plot2019.1.mw

WHY2019.1.mw

Maybe this helps

@Carl Love 

 

I honestly don't know why it worked.

First I tried Maple help: ?dsolve,system and I use option: useInt , but it dosen't work(bug or what?).If I use useint it worked.That's all.

@Bernard Afful 

Maybe this helps.

@minhthien2016 

 

restart;

Digits := 20;

sol := solve(simplify(expand(convert(sin(9*x - 1/3*Pi) = sin(5*x - 1/6*Pi), exp))), [x], explicit, allsolutions);

seq([x = simplify(allvalues(identify(evalf(simplify(Re(rhs(sol[j][1])))), all)))], j = 1 .. nops(sol));

#[x = Pi*_Z7 + 1/4*Pi], [x = Pi*_Z6 + 1/24*Pi], [x = Pi*_Z6 - 11/24*Pi], [x = Pi*_Z5 - 1/28*Pi], [x = Pi*_Z5 + 3/28*Pi], [x = #Pi*_Z5 + 11/28*Pi], [x = Pi*_Z5 - 13/28*Pi], [x = Pi*_Z5 - 9/28*Pi], [x = Pi*_Z5 - 5/28*Pi]

@Carl Love 

I copy and paste code to Maple and dosen't work?

@Carl Love 

It make sense to me.I don't  mean a discrete derivative.

@vv 

Yes I want differentiate with respect to a natural number.

@Rouben Rostamian

See attached file.
 

Download integral_ver2.mw

 

Yes, I also want  find many things?

Please post a clear example of input and desired output. Nobody likes to guess...

Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.

 You can upload a worksheet by using the green up-arrow on the toolbar of the MaplePrimes editor.

@golnaz 

You say:

 ((sqrt(a*e^(-2*x)+a))-sqrt(a)));

# Error, unable to match delimiters ???

You wrote in the question: (sqrt(exp(-2*x) + a) - sqrt(a)) then you wrote:  ((sqrt(a*e^(-2*x)+a))-sqrt(a))),it's not same expression ? 


 

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