テトレーション
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出典^ a b Goodstein, R. L. (1947). “Transfinite Ordinals in Recursive Number Theory”. The Journal of Symbolic Logic 12 (4): 123?129. doi:10.2307/2266486. .mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}ISSN 0022-4812. https://www.jstor.org/stable/2266486.
^ Maurer, Hans (1901). “Uber die Funktion y = x [ x [ x ( ⋯ ) ] ] {\displaystyle y=x^{[x^{[x(\cdots )]}]}} fur ganzzahliges Argument (Abundanzen)”. Mittheilungen der Mathematische Gesellschaft in Hamburg 4: 33–50.
^ Knoebel, R. Arthur (1981). “Exponentials Reiterated”. The American Mathematical Monthly 88 (4): 235?252. doi:10.2307/2320546. ISSN 0002-9890. https://www.jstor.org/stable/2320546.
^ Hooshmand, M. H. (2006-08-01). “Ultra power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8): 549?558. doi:10.1080/10652460500422247. ISSN 1065-2469. https://doi.org/10.1080/10652460500422247.
^ “ ⇒Exploding Array Function”. Jonathan Bowers. 2021年7月30日閲覧。
^ Daniel B. Shapiro and S. David Shapiro (2007). ⇒“Iterated Exponents in Number Theory” (pdf). Electronic Journal of Combinatorial Number Theory 7 (A23). ⇒http://math.colgate.edu/~integers/h23/h23.pdf 2021年7月30日閲覧。.
^ Jekusiel Ginsburg (1945). “Iterated Exponentials” (pdf). Scripa Mathematica 11: 340–353. https://oeis.org/A000405/a000405.pdf 2021年7月30日閲覧。.
^ Ioannis Galidakis. ⇒On Extending hyper4 and Knuth’s Up-arrow Notation to the Reals[リンク切れ]
^ “ ⇒Power Verb”. J Vocabulary. J Software. 2011年10月28日閲覧。
^ Edward Drake Roe, Jr. (1898). ⇒“68”. The American Mathematical Monthly 5: 110. doi:10.2307/2971013. ⇒http://www.jstor.org/stable/2971013.
^ I. N. Galidakis, (2004). ⇒“On an Application of Lambert’s W Function to Infinite Exponentials”. Complex Variables Th. Appl. 49: 759–780. doi:10.1080/02781070412331298796. ISSN 0278-1077. ⇒http://www.math.usm.edu/lee/InfiniteExponentials.pdf.
^ Euler, L., "De serie Lambertina Plurimisque eius insignibus proprietatibus." Acta Acad. Scient. Petropol. 2, 29–51, 1783. Reprinted in Euler, L. Opera Omnia, Series Prima, Vol. 6: Commentationes Algebraicae. Leipzig, Germany: Teubner, pp. 350–369, 1921. ( ⇒facsimile)
^ M. H. Hooshmand, (2006). “Ultra power and ultra exponential functions”. Integral Transforms and Special Functions（英語版） 17 (8): 549–558. doi:10.1080/10652460500422247.
^ Andrew Robbins. Solving for the Analytic Piecewise Extension of Tetration and the Super-logarithm
^ W. Paulsen and S. Cowgill (March 2017). ⇒“Solving F ( z + 1 ) = b F ( z ) {\displaystyle F(z+1)=b^{F(z)}} in the complex plane”. Advances in Computational Mathematics: 1-22. doi:10.1007/s10444-017-9524-1. ⇒http://link.springer.com/article/10.1007/s10444-017-9524-1.
^ ⇒テトレーションおよびその導関数を計算・描画するMathematicaコード
^ ⇒Marshall, Ash J., and Tan, Yiren, "A rational number of the form aa with a irrational", Mathematical Gazette 96, March 2012, pp. 106-109.
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