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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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0x2μνe14x2Mk,μ(12x2)Yν(xy)dx=π12μ+βykμ32e14y2Γ(2μ+1)×Γ(12kμ){cos[(ν2μ)π]Γ(2μν1)Γ(2β+1)Mα,β(12y2)sin[(ν+kμ)π]Wα,βπ(12y2)}?2α=3μν+k+12,??2β=μνk+12

si956_e  ET II 116(44)

[y>0,1<2Reμ<Re(2k+ν)+12,Re(2μν)>1]si957_e

14. 

0x2μ+νe14x2Mk,μ(12x2)Yν(xy)dx=π12μ+βykμ32Γ(2μ+1)×Γ(12μk)e14y2{cos(2μπ)Γ(2μ+ν+1)Γ(μ+νk+32)Mα,β(12y2)+sin[(μk)π]Wα,β(12y2)}2α=3μ+ν+k+12,2β=μ+νk+12

si958_e  ET II 116(43)

[y>0,1<2Reμ<Re(2kν)+12,Re(2μ+ν)>1]

15. 

0x2μ+

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