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...Richard Büchi]]. The [[signature (mathematical logic)|signature]] of Büchi arithmetic contains only the addition operation, <math>V_k</math> and equality, omitti ...chi arithmetic, whether that sentence is provable from the axioms of Büchi arithmetic. ...

...name="toth">{{cite journal |author=Lászlo Tóth |title=A survey of gcd-sum functions |journal=J. Integer Sequences |volume=13 |year=2010}}</ref> ...ana Pillai]] in 1933.<ref>{{cite journal |author=S. S. Pillai |title=On an arithmetic function |journal=Annamalai University Journal |volume=II |year=1933 |pages ...

==Non-arithmetic== ...s also possible to generalize the [[Geometric mean|''geometric'' mean]] to functions by: ...

{{Short description|Elementary functions and their finitely iterated integrals}} ...cursive definition|recursively defined]] as integrals of other Liouvillian functions. ...

...ref>Harvey Friedman. Classically and Intuitionistically Provably Recursive Functions. In Scott, D. S. and Muller, G. H. Editors, Higher Set Theory, Volume 699 o *Heyting arithmetic is closed under the primitive recursive Markov rule (MP_PR): if t ...

...ch&nbsp;1987). These degrees are closely related to fixed-point-free (DNR) functions, and have been thoroughly investigated in recursion theory. ...tion]] with index (program) ''e'' in some standard numbering of computable functions, and <math>\phi^B_e</math> denotes the ''e''th computable function using a ...

{{Short description|Mathematical method in elliptic functions}} ...ptic integral]], useful for the efficient numerical evaluation of elliptic functions. It was originally due to [[John Landen]] and independently rediscovered by ...

...heor. Verw. Geb.'', '''9''' : 3 (1968) pp. 163–195</ref><ref>R. Davidson, "Arithmetic and other properties of certain Delphic semi-groups" ''Z. Wahrscheinlichkei ...

In [[number theory]], a '''normal order of an arithmetic function''' is some simpler or better-understood function which "usually" t * [[Average order of an arithmetic function]] ...

...te=1975 |volume=40 |issue=3 |pages=347–382 }}</ref> or some [[Second-order arithmetic|higher-order arithmetics]]. ...y be denoted <math>{\mathrm {AC}}!</math>. It may also only be adopted for functions from the naturals to the naturals, then called <math>{\mathrm {AC}_{00}}!</ ...

{{Short description|System of arithmetic in proof theory}} {{redirect|Elementary recursive arithmetic|the computational complexity class|Elementary recursive function}} ...

{{Short description|Set of all true first-order statements about the arithmetic of natural numbers}} ...e set of all true [[first-order logic|first-order]] statements about the [[arithmetic]] of [[natural number]]s.<ref>{{Harvnb|Boolos|Burgess|Jeffrey|2002|p=295}}< ...

...nalysis]], a '''binade''' is a set of numbers in a binary [[Floating-point arithmetic|floating-point format]] that all have the same sign and exponent. |title=Handbook of Floating-Point Arithmetic ...

...onic mean]] can all be interpreted as Fréchet means for different distance functions. === Arithmetic mean and median === ...

== Interpretability of arithmetic == ...red Tarski|Tarski]] and [[Wanda Szmielew|Szmielew]] showed that [[Robinson arithmetic]] (<math>{\mathsf{Q}}</math>) can be interpreted in a weak set theory whose ...

...ion | last1=Lang | first1=Serge | author1-link=Serge Lang | title=Elliptic functions | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | [[Category:Modular arithmetic]] ...

{{Short description|Arithmetic function}} *[[Arithmetic function]] ...

...eorem in probabilistic number theory on additive complex-valued arithmetic functions}} ...theory]]. It is useful for proving results about the [[normal order of an arithmetic function]].<ref name="Tenenbaum" />{{Rp|305–308}} The theorem was proved in ...

{{Functions}} ...space|discrete]] and other [[totally disconnected space]]s integer-valued functions have roughly the same importance as [[real-valued function]]s have on non-d ...

...ithmetic/EA16CB4305831530B7015D6BC46B7424|title=Subsystems of Second Order Arithmetic|date=2009|publisher=Cambridge University Press|isbn=978-0-521-88439-6|editi {{Main article|2 = Buchholz psi functions}} ...