do we have relation between LommelS2 and MeijerG in matlab?

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gourav pandey 2021-1-25

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评论： Mubashara Wali 2021-4-5

Do we have matlab relation between two special function "LommelS2 and MeijerG"?

How to convert LommelS2 code into MeijerG?

Please help !!

回答（2 个）

Walter Roberson 2021-1-25

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编辑：Walter Roberson 2021-1-26

https://www.maplesoft.com/support/help/Maple/view.aspx?path=LommelS1

and scroll down to near the bottom to see the conversions.

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gourav pandey 2021-1-27

actually not completely.

fun1:=evalf(convert(LommelS2(-(1/2)*n-(1/2)*j+3/2, (1/2)*n+(1/2)*j+1/2, I*omega),MeijerG))assuming omega::real,0<omega;

fun1 := 0.00004212956333 + 0.00001923699304 I

fun2:=evalf(convert(LommelS2(-(1/2)*n-(1/2)*j+3/2, (1/2)*n+(1/2)*j+1/2, -I*omega),MeijerG))assuming omega::real,0<omega;

fun2 := 0.00004212956333 + 0.00001923699304 I

fun3:=evalf(LommelS2(-(1/2)*n-(1/2)*j+3/2, (1/2)*n+(1/2)*j+1/2, -I*omega));

fun3 := 0.00004212956330 - 0.00001923699311 I

fun4:=evalf(LommelS2(-(1/2)*n-(1/2)*j+3/2, (1/2)*n+(1/2)*j+1/2, I*omega));

fun4 := 0.4212956330e-4+0.1923699311e-4*I

as you suggested to get relation from MAPLE. so the above code is coded in maple. fun1 and fun2 are conjugate of eact other similarly fun3 and fun4. but we can see the difference in the answer of fun2 and fun3. you can see in BOLD letters.

fun1 and fun2 are converting the lommelS2 into MeijerG where fun3 and fun4 are directing calculating the lommelS2.

there is an issue with conjugate no. in MeijerG. do you know how to resolve this issue??

thank you!!

Walter Roberson 2021-4-5

I have corrected the ABC and regenerated the result. I had accidentally put in 1 - 1- alpha instead of 1 - alpha

Mubashara Wali 2021-4-5

Thankyou

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gourav pandey 2021-4-5

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https://ww2.mathworks.cn/matlabcentral/answers/726363-do-we-have-relation-between-lommels2-and-meijerg-in-matlab#answer_667012

编辑：gourav pandey 2021-4-5

在 MATLAB Online 中打开

Walter Roberson, thanks for your reply..can you help me here also

clc;
close;
clear all;
n=5;
h=@(omega1) 0;
   for m= 0:1:n
        mu1c = -(1./2).*n-(1./2).*m+3./2 ;
        nu1c =  (1./2).*n+(1./2).*m+1./2 ; 
       Lommels =@(omega1) meijerG([(1./2).*mu1c+1./2], [], [(1./2).*mu1c+1./2, (1./2).*nu1c, -(1./2).*nu1c], [], -(1./4).*omega1.^2).*2^mu1c./(2.*gamma(-(1./2).*mu1c+(1./2).*nu1c+1./2).*gamma(-(1./2).*mu1c-(1./2).*nu1c+1./2))
   end
Lommels(1)
Lommels(10)
Lommels(99)
Lommels(100)
Lommels(500)
Lommels(1000)