Why I am not able to do the integration??
1 次查看(过去 30 天)
显示 更早的评论
%%%%%%%%% Integration w.r.t 'omega1'
%% Thank you in Advance!!
int((exp(-2*abs(omega1))*((4*2^(1/2)*(2^(1/2)*abs(omega1)^(3/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(6352209995579977/36028797018963968 + 6352209995579977i/36028797018963968) + 2^(1/2)*abs(omega1)^(5/2)*meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4)*(5081767996463981/144115188075855872 - 5081767996463981i/144115188075855872) + 2^(1/2)*abs(omega1)^(3/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(3176104997789989/18014398509481984 - 794026249447497i/4503599627370496) + 2^(1/2)*abs(omega1)^(5/2)*conj(meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4))*(5081767996463981/144115188075855872 + 5081767996463983i/144115188075855872)))/abs(omega1) + (13*2^(1/2)*sign(omega1)*(2^(1/2)*abs(omega1)^(1/2)*meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4)*(1905662998673993/9007199254740992 + 1905662998673993i/9007199254740992) + 2^(1/2)*abs(omega1)^(3/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(5081767996463981/72057594037927936 - 5081767996463981i/72057594037927936) - 2^(1/2)*abs(omega1)^(1/2)*conj(meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4))*(1905662998673993/9007199254740992 - 1905662998673993i/9007199254740992) - 2^(1/2)*abs(omega1)^(3/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(5081767996463981/72057594037927936 + 5081767996463981i/72057594037927936)))/10 + (39*2^(1/2)*sign(omega1)*(abs(omega1)^(5/2)*(2^(1/2)*meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4)*(5081767996463981/72057594037927936 - 5081767996463981i/72057594037927936) + 2^(1/2)*conj(meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4))*(5081767996463981/72057594037927936 + 5081767996463981i/72057594037927936))*1i - 2^(1/2)*abs(omega1)^(3/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(6352209995579977/18014398509481984 - 6352209995579977i/18014398509481984) + 2^(1/2)*abs(omega1)^(3/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(794026249447497/2251799813685248 + 3176104997789989i/9007199254740992)))/40 - (13*2^(1/2)*sign(omega1)*(2^(1/2)*abs(omega1)^(5/2)*meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4)*(2171165525833/35184372088832 + 2171165525833i/35184372088832) + 2^(1/2)*abs(omega1)^(7/2)*meijerG(-3/4, [], [-9/4, -3/4, 9/4], [], -omega1^2/4)*(5081767996463981/576460752303423488 - 5081767996463981i/576460752303423488) - 2^(1/2)*abs(omega1)^(5/2)*conj(meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4))*(8893093993811969/144115188075855872 - 4446546996905983i/72057594037927936) - 2^(1/2)*abs(omega1)^(7/2)*conj(meijerG(-3/4, [], [-9/4, -3/4, 9/4], [], -omega1^2/4))*(1270441999115995/144115188075855872 + 2540883998231991i/288230376151711744)))/15 + (13*abs(omega1)^(7/2)*sign(omega1)*(conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(5081767996463981/72057594037927936 + 5081767996463981i/72057594037927936) - meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(5081767996463981/72057594037927936 - 5081767996463981i/72057594037927936)))/60 - (2^(1/2)*(2^(1/2)*abs(omega1)^(1/2)*meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4)*(1905662998673993/9007199254740992 - 1905662998673993i/9007199254740992) - 2^(1/2)*abs(omega1)^(3/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(5081767996463981/72057594037927936 + 5081767996463981i/72057594037927936) + 2^(1/2)*abs(omega1)^(1/2)*conj(meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4))*(1905662998673993/9007199254740992 + 1905662998673993i/9007199254740992) - 2^(1/2)*abs(omega1)^(3/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(5081767996463981/72057594037927936 - 5081767996463981i/72057594037927936)))/(2*abs(omega1)) + (2^(1/2)*(2^(1/2)*abs(omega1)^(1/2)*meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4)*(1905662998673993/4503599627370496 - 1905662998673993i/4503599627370496) - 2^(1/2)*abs(omega1)^(3/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(5081767996463981/36028797018963968 + 5081767996463981i/36028797018963968) + 2^(1/2)*abs(omega1)^(1/2)*conj(meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4))*(1905662998673993/4503599627370496 + 1905662998673993i/4503599627370496) - 2^(1/2)*abs(omega1)^(3/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(5081767996463981/36028797018963968 - 5081767996463981i/36028797018963968)))/(4*abs(omega1)) + (4*2^(1/2)*(2^(1/2)*abs(omega1)^(5/2)*meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4)*(2171165525833/35184372088832 - 2171165525833i/35184372088832) - 2^(1/2)*abs(omega1)^(7/2)*meijerG(-3/4, [], [-9/4, -3/4, 9/4], [], -omega1^2/4)*(5081767996463981/576460752303423488 + 5081767996463981i/576460752303423488) + 2^(1/2)*abs(omega1)^(5/2)*conj(meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4))*(4446546996905983/72057594037927936 + 8893093993811969i/144115188075855872) - 2^(1/2)*abs(omega1)^(7/2)*conj(meijerG(-3/4, [], [-9/4, -3/4, 9/4], [], -omega1^2/4))*(2540883998231991/288230376151711744 - 1270441999115995i/144115188075855872)))/abs(omega1) + (2^(1/2)*abs(omega1)^(3/2)*(2^(1/2)*meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4)*(5081767996463981/36028797018963968 - 5081767996463981i/36028797018963968) + 2^(1/2)*conj(meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4))*(5081767996463981/36028797018963968 + 5081767996463981i/36028797018963968)))/8 - (2^(1/2)*abs(omega1)^(3/2)*(2^(1/2)*meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4)*(5081767996463981/36028797018963968 + 5081767996463981i/36028797018963968) - 2^(1/2)*conj(meijerG(3/4, [], [-3/4, 3/4, 3/4], [], -omega1^2/4))*(5081767996463981/36028797018963968 - 5081767996463981i/36028797018963968))*5i)/8 - (2^(1/2)*abs(omega1)^(5/2)*(2^(1/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(5081767996463981/72057594037927936 - 5081767996463981i/72057594037927936) - 2^(1/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(5081767996463981/72057594037927936 + 5081767996463981i/72057594037927936))*1i)/4 - (2^(1/2)*abs(omega1)^(5/2)*(2^(1/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(5081767996463981/72057594037927936 + 5081767996463981i/72057594037927936) + 2^(1/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(5081767996463981/72057594037927936 - 5081767996463981i/72057594037927936)))/4 - (2^(1/2)*abs(omega1)^(7/2)*(2^(1/2)*meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4)*(5081767996463981/288230376151711744 - 5081767996463981i/288230376151711744) + 2^(1/2)*conj(meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4))*(5081767996463981/288230376151711744 + 5081767996463981i/288230376151711744)))/3 - (2^(1/2)*abs(omega1)^(7/2)*(2^(1/2)*meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4)*(5081767996463981/288230376151711744 + 5081767996463981i/288230376151711744) - 2^(1/2)*conj(meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4))*(5081767996463981/288230376151711744 - 5081767996463981i/288230376151711744))*1i)/3 + (39*2^(1/2)*sign(omega1)*(2^(1/2)*abs(omega1)^(3/2)*meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4)*(6352209995579977/36028797018963968 - 6352209995579977i/36028797018963968) - 2^(1/2)*abs(omega1)^(5/2)*meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4)*(5081767996463981/144115188075855872 + 5081767996463981i/144115188075855872) - 2^(1/2)*abs(omega1)^(3/2)*conj(meijerG(1/4, [], [-5/4, 1/4, 5/4], [], -omega1^2/4))*(794026249447497/4503599627370496 + 3176104997789989i/18014398509481984) + 2^(1/2)*abs(omega1)^(5/2)*conj(meijerG(-1/4, [], [-7/4, -1/4, 7/4], [], -omega1^2/4))*(5081767996463983/144115188075855872 - 5081767996463981i/144115188075855872)))/20))/omega1^2, omega1, -2, 2)
2 个评论
David Goodmanson
2021-4-15
编辑:David Goodmanson
2021-4-15
Hello gourav,
Not every function has an analytic solution for its integral, and this one with all the Meijer G functions is so complicated that it probably does not. Sometimes we just have to take the bitter with the sweet. Anyway, there are problems for other reasons.
The integrand is complex and appears to have a singularity at the origin. As you approach the origin, the abs value goes like omega1^(-2) for awhile, and then for omega1 less than 1e-7 it goes as omega1^(-4). I don't know whether the latter behavior is due to numerical reasons, but let's say it is. However, the omega1^(-2) behavior by itself is enough to produce an infinite integral unless there is a rapidly oscillating phase factor to level out the singularity, and there is no sign of that happening.
回答(0 个)
另请参阅
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!