Question Number 93546 by allizzwell23 last updated on 13/May/20
$$\:\:\mathrm{Which}\:\mathrm{app}\:\mathrm{is}\:\mathrm{the}\:\mathrm{best}\:\mathrm{to}\:\mathrm{evaluate} \\ $$$$\:\:\:\:\frac{\mathrm{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)}{\mathrm{ln}\:\mathrm{2}} \\ $$
Commented by IbrahimGR376 last updated on 13/May/20
$$\:\:\:\mathrm{mathematica}\:\mathrm{app}\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{GR376} \\ $$
Commented by prakash jain last updated on 13/May/20
https://www.wolframalpha.com
Commented by allizzwell23 last updated on 13/May/20
$$\mathrm{i}\:\mathrm{dont}\:\mathrm{know}\:\mathrm{how}\:\mathrm{to}\:\mathrm{input}\:\mathrm{correctly} \\ $$
Commented by prakash jain last updated on 13/May/20
in wolfram alpha. You can simply write plain text W(2ln2)/ln2
Commented by allizzwell23 last updated on 13/May/20
$$\mathrm{yes}\:\mathrm{sir}.\:\mathrm{can}\:\mathrm{you}\:\mathrm{show}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to}\:\mathrm{use}\:\mathrm{it} \\ $$
Commented by prakash jain last updated on 13/May/20
Wolfram alpha is just plain text input
Commented by prakash jain last updated on 13/May/20
Wolfram will give alternate implementations of W. It will hive u options to select. for specific interpretations you can lambertw(2ln2)/ln2. or eta(5) or theta(5)
Commented by allizzwell23 last updated on 13/May/20
$$\mathrm{thanks}\:\mathrm{sir} \\ $$
Commented by mr W last updated on 13/May/20
$${be}\:{careful}: \\ $$$${for}\:{x}<\mathrm{0},\:{wolframalpha}\:{gives}\:{only} \\ $$$${one}\:{value}\:{of}\:{W}\left({x}\right).\:{for}\:{example}: \\ $$$${W}\left(−\mathrm{0}.\mathrm{1}\right)=−\mathrm{0}.\mathrm{111833}\:{or}\:−\mathrm{3}.\mathrm{577152}. \\ $$$${but}\:{wolframalpha}\:{gives}\:{only} \\ $$$${W}\left(−\mathrm{0}.\mathrm{1}\right)=−\mathrm{0}.\mathrm{111833} \\ $$
Commented by mr W last updated on 13/May/20
$${but}\:{if}\:{you}\:{just}\:{want}\:{to}\:{get}\:\frac{{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)}{\mathrm{ln}\:\mathrm{2}}, \\ $$$${you}\:{don}'{t}\:{need}\:{any}\:{app}.\:{it}\:{is}\:\mathrm{1}. \\ $$$${i}.{e}.\:\frac{{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)}{\mathrm{ln}\:\mathrm{2}}=\mathrm{1}. \\ $$$${how}? \\ $$$${ac}.\:{to}\:{definition}: \\ $$$${W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right){e}^{{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)} =\mathrm{2}\:\mathrm{ln}\:\mathrm{2}=\left(\mathrm{ln}\:\mathrm{2}\right){e}^{\left(\mathrm{ln}\:\mathrm{2}\right)} \\ $$$$\Rightarrow{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)=\mathrm{ln}\:\mathrm{2} \\ $$$$\Rightarrow\frac{{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)}{\mathrm{ln}\:\mathrm{2}}=\mathrm{1} \\ $$
Commented by prakash jain last updated on 13/May/20
$${ye}^{{y}} ={x} \\ $$$${x}\geqslant\mathrm{0}\:\mathrm{we}\:\mathrm{get}\:\mathrm{one}\:\mathrm{value}\:\mathrm{for}\:{y}\mathrm{which} \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{W}_{\mathrm{0}} \left({x}\right) \\ $$$$−\frac{\mathrm{1}}{{e}}\leqslant{x}<\mathrm{0} \\ $$$$\mathrm{We}\:\mathrm{get}\:\mathrm{two}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{which} \\ $$$$\mathrm{are}\:\mathrm{given}\:{W}_{\mathrm{0}} \left({x}\right)\:\mathrm{and}\:{W}_{−\mathrm{1}} \left({x}\right) \\ $$$$\mathrm{Wolform}\:\mathrm{will}\:\mathrm{correctly}\:\mathrm{give} \\ $$$$\mathrm{two}\:\mathrm{results}\:\mathrm{when}\:\mathrm{you}\:\mathrm{ask}\:\mathrm{it} \\ $$$$\mathrm{to}\:\mathrm{solve}\:{xe}^{{x}} =−.\mathrm{1} \\ $$$$\mathrm{but}\:{W}\left({x}\right)\:\mathrm{it}\:\mathrm{will}\:\mathrm{interpret}\:\mathrm{as}\:{W}_{\mathrm{0}} \left({x}\right) \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{a}\:\mathrm{single}\:\mathrm{valued}\:\mathrm{function} \\ $$$$\mathrm{for}\:{x}=−.\mathrm{1} \\ $$
Commented by allizzwell23 last updated on 13/May/20
$$\mathrm{thanks} \\ $$
Commented by mr W last updated on 13/May/20
$${thanks}\:{for}\:{the}\:{explanation}\:{sir}! \\ $$