Partial Values for Knuth's Up-Arrows
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$3 uparrow 4 $ is $3^4$, and $3uparrow uparrow 3$ is $3^{3^{3^3}}$, etc. For those of you unfamiliar, here is a wiki page on the notation. Clearly, up-arrow expressions, as they are usually defined, only have meaning when the number of arrows is in the naturals. Is there an extension, similar to $Gamma (x)$ and the factorial function, that extends this to all reals, or even complex?
power-towers
asked 12 hours ago
William Grannis
741418
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up vote
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$3 uparrow 4 $ is $3^4$, and $3uparrow uparrow 3$ is $3^{3^{3^3}}$, etc. For those of you unfamiliar, here is a wiki page on the notation. Clearly, up-arrow expressions, as they are usually defined, only have meaning when the number of arrows is in the naturals. Is there an extension, similar to $Gamma (x)$ and the factorial function, that extends this to all reals, or even complex?
power-towers
asked 12 hours ago
William Grannis
741418
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
$3 uparrow 4 $ is $3^4$, and $3uparrow uparrow 3$ is $3^{3^{3^3}}$, etc. For those of you unfamiliar, here is a wiki page on the notation. Clearly, up-arrow expressions, as they are usually defined, only have meaning when the number of arrows is in the naturals. Is there an extension, similar to $Gamma (x)$ and the factorial function, that extends this to all reals, or even complex?
power-towers
asked 12 hours ago
William Grannis
741418
$3 uparrow 4 $ is $3^4$, and $3uparrow uparrow 3$ is $3^{3^{3^3}}$, etc. For those of you unfamiliar, here is a wiki page on the notation. Clearly, up-arrow expressions, as they are usually defined, only have meaning when the number of arrows is in the naturals. Is there an extension, similar to $Gamma (x)$ and the factorial function, that extends this to all reals, or even complex?
power-towers
power-towers
asked 12 hours ago
William Grannis
741418
asked 12 hours ago
William Grannis
741418
asked 12 hours ago
William Grannis
741418
asked 12 hours ago
William Grannis
741418
asked 12 hours ago
William Grannis
741418
741418
add a comment |
add a comment |
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