Negative parameters of Mejier G function

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Ali Akber 2017-3-17

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https://ww2.mathworks.cn/matlabcentral/answers/330316-negative-parameters-of-mejier-g-function

评论： Walter Roberson 2017-3-18

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Dear Users

Is it possible that meijerG function contain a negative value (i.e. is {-1,0,0})? I tried both Mathematica and Matlab to compute this meijerG function but they generate error that this "meijerG is not defined for the given parameters" Any help will be helpful. Here is my code

        D = (0.6);
        lg1 = lg2 = 1;
        G = evalin(symengine, sprintf('meijerG([[0], []], [[-1,0,0], []],%f)',(D/(lg1*lg2))));
        CD = -((2*D)/(lg1*lg2*(log(4))))*G;

Regards

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Walter Roberson 2017-3-17

Is that K0 the BesselK function?

Ali Akber 2017-3-17

Yes, it is modified Bessel function of the second kind

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Walter Roberson 2017-3-17

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https://ww2.mathworks.cn/matlabcentral/answers/330316-negative-parameters-of-mejier-g-function#answer_259105

编辑：Walter Roberson 2017-3-17

As I indicated before, 0 from the first argument, minus negative 1 from the second argument, gives +1,a positive integer. MeijerG is not defined when one of those differences is a positive integer. There is no way to make such a calculation. You should look up the definition of meijerg and you will see this described.

It is not a limitation of MATLAB or Mathematica or Maple, not a case where "it is just really tough to calculate so we have not bothered": it is fundamental to MeijerG's definition.

Note that it is not a difficulty with negative parameters themselves. You would have the same problem if you for example had 4 in the first parameter and 2 in the second parameter: the difference would be a positive integer and that is not permitted for the function to have meaning. If the first parameter was, for example, 1/2 then -1 would be fine in the second parameter.

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Ali Akber 2017-3-18

Ohh wawo.. Can you elaborate this a little more? Which function you exactly evaluated? If possible please share the Maple code. I would be very thankful.

Regards

Walter Roberson 2017-3-18

在 MATLAB Online 中打开

The Maple code was:

T := 2*b*BesselK(0, sqrt(4*b*Gamma/(lambda__g*lambda__h)))*log[2](1+Gamma)/(lambda__g*lambda__h);
U := solve(x = sqrt(4*b*Gamma/(lambda__g*lambda__h)), Gamma);
simplify(eval(T,Gamma=U)) assuming x >= 0;
int(%,x=0..infinity);
simplify(%) assuming nonnegative;