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F j ( x ) := ( 1 / Γ ( j + 1 ) ) ∫ 0 ∞ d t ( t j / ( exp ( t − x ) + 1 ) ) {\displaystyle F_{j}(x):=(1/\Gamma (j+1))\int _{0}^{\infty }dt(t^{j}/(\exp(t-x)+1))}
F j ( x , b ) := ( 1 / Γ ( j + 1 ) ) ∫ b ∞ d t ( t j / ( exp ( t − x ) + 1 ) ) {\displaystyle F_{j}(x,b):=(1/\Gamma (j+1))\int _{b}^{\infty }dt(t^{j}/(\exp(t-x)+1))}
A i ( x ) = ( 1 / π ) ∫ 0 ∞ cos ( ( 1 / 3 ) t 3 + x t ) d t {\displaystyle Ai(x)=(1/\pi )\int _{0}^{\infty }\cos((1/3)t^{3}+xt)dt} B i ( x ) = ( 1 / π ) ∫ 0 ∞ ( e ( − ( 1 / 3 ) t 3 ) + sin ( ( 1 / 3 ) t 3 + x t ) ) d t {\displaystyle Bi(x)=(1/\pi )\int _{0}^{\infty }(e^{(}-(1/3)t^{3})+\sin((1/3)t^{3}+xt))dt}
