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{{Short description|Term used in transcendental number theory}} ...mr=997310}}</ref> It marked a breakthrough in the theory of transcendental numbers. Many longstanding open problems can be deduced as direct consequences. ...

...[mathematics]], the '''Siegel G-functions''' are a class of functions in [[transcendental number theory]] introduced by [[C. L. Siegel]]. They satisfy a [[linear di [[Category:Transcendental numbers]] ...

...restrictions on possible values of [[L2 cohomology|<math>l^2</math>-Betti numbers]]. ...ed if it is possible for <math>l^2</math>-Betti numbers to be [[irrational numbers|irrational]]. ...

...and ''b'' is a real [[quadratic irrational]], are [[transcendental number|transcendental]]. In particular, this result implies that [[Gelfond–Schneider constant]] :is transcendental. See [[Gelfond–Schneider theorem]] for later developments. ...

...urnal|last=Feldman|first=Naum|date=2000|title=Algebraic and transcendental numbers|url=http://static.nsta.org/pdfs/QuantumV10N6.pdf|journal=Quantum|volume=10| ...9|bibcode=1967RuMaS..22....1F}}</ref><ref>{{cite book|title=Transcendental Numbers|url=https://archive.org/details/numbertheorytran00pars|url-access=limited|l ...

| title = Expression of real numbers with the help of infinite series {{harvtxt|Hančl|1996}} has defined a transcendental sequence to be an integer sequence ''a''_''n'' such that, for eve ...

...ion|Dirichlet {{mvar|L}}-function]] for the field of [[Gaussian rational]] numbers. This formula is a special case of the [[analytic class number formula]], a ...anscendental" number (regardless of whether it is currently possible for [[transcendental number theory]] to provide a proof of the transcendence); and</li> ...

...on effective methods in number theory, in particular those arising from [[transcendental number theory]]. His interests were in number theory, [[Transcendental number theory|transcendence]], [[linear forms in logarithms]], [[Effective ...

...arvtxt| Lang|1966}} of a theorem of {{harvtxt|Schneider|1949}} about the [[transcendental number|transcendence]] of values of [[meromorphic function]]s. The theorem ...plies the [[Hermite–Lindemann theorem]] that {{math|''e^α''}} is transcendental for nonzero [[algebraic number|algebraic]] {{mvar|α}}: otherwise, {{math|'' ...

...are about solvability of (systems of) polynomial equations in the complex numbers. ...braic Closedness''' and covers the case of Existential Closedness when the transcendental function involved is the complex exponential function. It was later general ...

...hat is, it is generally the sum of [[unit fraction]]s. If infinitely many numbers have their reciprocals summed, generally the terms are given in a certain s If only finitely many numbers are included, the key issue is usually to find a simple expression for the ...

...n 1990 by [[Ekaterina Karatsuba]]<ref>E. A. Karatsuba, Fast evaluations of transcendental functions. Probl. Peredachi Informat., Vol. 27, No. 4, (1991)</ref><ref>D. ''Transcendental numbers''. Princeton University Press, Princeton (1949).</ref> Among these function ...

...first part and 22 chapters in the second. It has [[Eneström index|Eneström numbers]] E101 and E102.<ref>{{Cite web|url=https://scholarlycommons.pacific.edu/eu ...ifferentiation or integration. In particular, he introduced the elementary transcendental functions, the logarithm, the exponential function, the trigonometric funct ...

...umber problem]] of finding all imaginary [[quadratic field]]s with [[Class numbers of imaginary quadratic fields|class number]] 1. ...comes the statement that any nonzero element of <math>\mathbb{L}</math> is transcendental. ...

...no formal statement as such but refers to a general problem prevalent in [[transcendental number theory]]. Often proofs in transcendence theory are [[Reductio ad ab ...

...st one of the two numbers <math>e^e</math> and <math>e^{e^2}</math> is a [[transcendental number]]; here <math>e</math> denotes [[e (mathematical constant)|Euler's n | title = On the numbers <math>e^e</math>, <math>e^{e^2}</math> and <math>e^{\pi^2}</math> ...

...math>k=n=0</math> equals 1. Special values, where all contributing Catalan numbers equal 1, are ...de:Fritz Oberhettinger |last4=Tricomi | first4=Francesco G. | title=Higher transcendental functions. Vol. III | publisher=McGraw-Hill Book Company, Inc. |place= New ...

{{Short description|Irrational numbers which appear to be rational}} The sequence of numbers generated by the recurrence relation {{nowrap|1=''f''&hairsp;(''n'') = 10 ' ...

...ral numbers. Natural numbers including 0 are also sometimes called ''whole numbers''.<ref> ...ath>\mathbb{Z}</math>): Positive and [[negative number|negative]] counting numbers, as well as zero: {..., −3, −2, −1, 0, 1, 2, 3, ...}. ...

...nontrivial]] example of a universal attracting fixed point. It is also a [[transcendental number]] because of the [[Lindemann–Weierstrass theorem]].<ref>{{cite web|u ...lator is set to take angles in [[degree (angle)|degrees]], the sequence of numbers will instead converge to <math>0.999847...</math>,<ref>{{Cite OEIS|A330119} ...