Painlevé Transcendents - 32.5 Integral Equations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
32.5.E1	${\displaystyle{\displaystyle K(z,\zeta)=k\mathrm{Ai}\left(\frac{z+\zeta}{2}\right)+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\mathrm{Ai}\left(\frac{s+t}{2}\right)\mathrm{Ai}\left(\frac{t+\zeta}{2}\right)\mathrm{d}s\mathrm{d}t}}$ K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}		K(z , zeta) = k*AiryAi((z + zeta)/(2))+((k)^(2))/(4)* int(int(K(z , s)* AiryAi((s + t)/(2))*AiryAi((t + zeta)/(2)), s = z..infinity), t = z..infinity)	K[z , \[Zeta]] == k*AiryAi[Divide[z + \[Zeta],2]]+Divide[(k)^(2),4]* Integrate[Integrate[K[z , s]* AiryAi[Divide[s + t,2]]*AiryAi[Divide[t + \[Zeta],2]], {s, z, Infinity}, GenerateConditions->None], {t, z, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Error
32.5.E2	${\displaystyle{\displaystyle w(z)=K(z,z)}}$ w(z) = K(z,z)		w(z) = K(z , z)	w[z] == K[z , z]	Skipped - no semantic math	Skipped - no semantic math	-	-