User blog comment:Denis Maksudov/M-notation (M-function)/@comment-11227630-20160611023101/@comment-28606698-20160611212733

fω(x) = fx(x)

f ω2(x) = f ω+x(x)

f ω^2(x) = f ω<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">*<span style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast">ω<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">(x) = f <span style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast">ω<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">x<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">(x)

<p class="MsoNormal" style="margin-bottom:0.0001pt;"><span style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast">fω^3(x) = f(ω^2)x(x) <span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">

<p class="MsoNormal" style="margin-bottom:0.0001pt;"><span lang="EN-US" style="font-family:"TimesNewRoman","serif"; mso-fareast-font-family:"TimesNewRoman";mso-fareast-theme-font:minor-fareast; mso-ansi-language:EN-US">f <span style="font-family:"TimesNewRoman","serif"; mso-fareast-font-family:"TimesNewRoman";mso-fareast-theme-font:minor-fareast">ε<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">(0)<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">(x) = f <span style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast">ω<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">^(<span style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast">ω<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">^(<span style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast">ω<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">^(…x<span style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast">ω<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family:"TimesNewRoman"; mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">'s… )))<span lang="EN-US" style="font-family:"TimesNewRoman","serif";mso-fareast-font-family: "TimesNewRoman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US">(x)

<p class="MsoNormal" style="margin-bottom:0.0001pt;"><span lang="EN-US" style="font-family:"TimesNewRoman","serif"; mso-fareast-font-family:"TimesNewRoman";mso-fareast-theme-font:minor-fareast; mso-ansi-language:EN-US">ω↑ ω= ω^ω ω^(

<p class="MsoNormal" style="margin-bottom:0.0001pt;"><span lang="EN-US" style="font-family:"TimesNewRoman","serif"; mso-fareast-font-family:"TimesNewRoman";mso-fareast-theme-font:minor-fareast; mso-ansi-language:EN-US">ω↑^2  ω= ω↑↑ ω= ω^( ω^(… )=ε0

<p class="MsoNormal" style="margin-bottom:0.0001pt;"><span lang="EN-US" style="font-family:"TimesNewRoman","serif"; mso-fareast-font-family:"TimesNewRoman";mso-fareast-theme-font:minor-fareast; mso-ansi-language:EN-US">ω↑^3  ω= ω↑↑↑ω= ζ0

<p class="MsoNormal" style="margin-bottom:0.0001pt;"><span lang="EN-US" style="font-family:"TimesNewRoman","serif"; mso-fareast-font-family:"TimesNewRoman";mso-fareast-theme-font:minor-fareast; mso-ansi-language:EN-US">ω↑^4  ω= ω↑↑↑↑ω= η0

<p class="MsoNormal" style="margin-bottom:0.0001pt;"><span lang="EN-US" style="font-family:"TimesNewRoman","serif"; mso-ansi-language:EN-US">And so on

<p class="MsoNormal" style="margin-bottom:0.0001pt;">