2^z == z/(1 + z/(Abs[(-(1/2))^z] + z/(6^(-Re[z]) + z/(z/(Abs[(-(1/30))^z] + \[Ellipsis]))))) /; Re[z] > 0

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mn> 2 </mn> <mi> z </mi> </msup> <mo> &#10869; </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> z </mi> </msup> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <msup> <mn> 6 </mn> <mrow> <mo> - </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </msup> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 30 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> z </mi> </msup> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <abs /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <real /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <abs /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 30 </cn> </apply> <ci> z </ci> </apply> </apply> <ci> &#8230; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <gt /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29