theory, a nonelementary problem is a problem that is not a member of the class ELEMENTARY. As a class it is sometimes denoted as NONELEMENTARY. Examples...

results on how much to implement this problem in practice. In 2018, the problem was shown to be a nonelementary problem. In 2022 it was shown to be complete...

In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary...

1954, this proof appeared in the book of Akiva and Isaak Yaglom "Nonelementary Problems in an Elementary Exposition". Later, in 1982, it appeared in the...

antiderivatives of elementary functions can be expressed as elementary functions Nonelementary integral – Integrals not expressible in closed-form from elementary...

nets was known to be EXPSPACE-hard for a long time, but shown to be nonelementary, so probably not in EXPSPACE. In 2022 it was shown to be Ackermann-complete...

function Lists of integrals Liouville's theorem (differential algebra) Nonelementary integral Symbolic integration Geddes, Czapor & Labahn 1992. Miller,...

undecidable for ATAs, but decidable for OCATAs, though it[ambiguous] is a nonelementary problem. Lasota, SƗawomir; Walukiewicz, Igor (2008). "Alternating Timed...

is hidden in the nonelementary integral (nonelementary unless C 0 = 2 {\displaystyle C_{0}=2} ). Another way to approach the problem is to linearize any...

cannot themselves be expressed as elementary functions. These are called nonelementary antiderivatives. A standard example of such a function is e − x 2 ,...

immediately obvious, but can be proven using the Risch algorithm. other nonelementary integrals, including the Dirichlet integral and elliptic integral. It...

theories (S2S, S1S, WS2S, WS1S), the complexity of the decision problem is nonelementary. Monadic second-order logic of trees has applications in formal...

be in neither.) "The hardest problems" of a class refer to problems which belong to the class such that every other problem of that class can be reduced...

Riemann Integral Trapezoidal rule Romberg's method Tanh-sinh quadrature Nonelementary Integral Weisstein, Eric W. "Cubature". MathWorld. "Earliest Known Uses...

Reachability in vector addition systems is Ackermann-complete (and hence nonelementary). A vector addition system consists of a finite set of integer vectors...

integrals that can be expressed in closed form. See antiderivative and nonelementary integral for more details. A procedure called the Risch algorithm exists...

July 18, 2018. NOTE: Adult education, community services and other nonelementary-secondary program expenditures are excluded. Gordon, Tracy; Iselin,...

the factor of 2 π {\displaystyle {\frac {2}{\sqrt {\pi }}}} . This nonelementary integral is a sigmoid function that occurs often in probability, statistics...

using quantifier elimination. The complexity of the decision problem is in NONELEMENTARY because binary constructors are injective and thus pairing functions...

limits List of mathematical identities List of mathematical series Nonelementary integral – Integrals not expressible in closed-form from elementary...

Alternative methods exist to compute more complex integrals. Many nonelementary integrals can be expanded in a Taylor series and integrated term by...

{L}}_{\text{rcf}}} . Tarski's original algorithm for quantifier elimination has nonelementary computational complexity, meaning that no tower 2 2 ⋅ ⋅ ⋅ n {\displaystyle...

{6A}{5}}y^{5/3}+C_{0}}}}=t} This is an implicit solution which involves a nonelementary integral. This same method is used to solve the period of a simple pendulum...

Retrieved 2018-07-18. NOTE: Adult education, community services and other nonelementary-secondary program expenditures are excluded. Gordon, Tracy; Iselin,...

These response-model equations are quite complicated and some involve a nonelementary integral; the exact solutions can be found here. It is shown here, however...