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Question Number 80131 by M±th+et£s last updated on 31/Jan/20

Commented by MJS last updated on 31/Jan/20

+∞  e^(π/2) ≈4.8  4.8^(4.8) ≈1913  ...

+eπ24.84.84.81913...

Commented by mr W last updated on 31/Jan/20

do you mean e^(−(π/2)) ? then:  (e^(−(π/2)) )^(....) =x  (e^(−(π/2)) )^x =x  e^(−((πx)/2)) =x  ((πx)/2)e^((πx)/2) =(π/2)  ((πx)/2)=W((π/2))  ⇒x=(2/π)W((π/2))≈((2×0.7454)/π)=0.4745

doyoumeaneπ2?then:(eπ2)....=x(eπ2)x=xeπx2=xπx2eπx2=π2πx2=W(π2)x=2πW(π2)2×0.7454π=0.4745

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