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Analysis of Transcendental Number
International Journal of Innovative Science and Research TechnologyThe complex realm of transcendental numbers is examined in this subject, along with its characteristics, relationships to other branches of mathematics, and practical uses. The study starts with a summary of transcendental number theory, including its historical evolution, salient characteristics, and important mathematical applications.
Suman Rani, Sunita
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A lemma in transcendental number theory [PDF]
Transactions of the American Mathematical Society, 1969 "LEMMA. Suppose p, q, p > qY, r, r, are positive rational integers, e> 0 and y are fixed, and all the numbers a1, aM2, ..., 9 'Mq, as well as the numbers P12, 2 . .P Pr are distinct and arranged in order of increasing absolute values, in other words, lakl _I lak+1I and |Pk| _ jIk+11. We set Ia,qI =,a, I PrI =P and suppose that there exist constants yo >
Robert Spira
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On the Number of Solutions of a Transcendental Equation Arising in the Theory of Gravitational Lensing [PDF]
, 2010 The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions.
Walter Bergweiler +3 more
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A Survey of Some Recent Developments on Higher Transcendental Functions of Analytic Number Theory and Applied Mathematics [PDF]
Symmetry, 2021 Often referred to as special functions or mathematical functions, the origin of many members of the remarkably vast family of higher transcendental functions can be traced back to such widespread areas as (for example) mathematical physics, analytic ...
H. M. Srivastava
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Journal of Advances in Mathematics and Computer Science, 2021 In this paper intuitionistic set theory INC#∞# in infinitary set theoretical language is considered. External induction principle in nonstandard intuitionistic arithmetic were derived.
Jaykov Foukzon
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On the number of solutions of some transcendental equations [PDF]
, 2017 We give upper and lower bounds for the number of solutions of the equation $$p(z)\log |z|+q(z)=0$$p(z)log|z|+q(z)=0 with polynomials p and q.
Walter Bergweiler, Alexandre Erëmenko
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Mathematics, 2021 A system of transcendental equations (SoTE) is a set of simultaneous equations containing at least a transcendental function. Solutions involving transcendental equations are often problematic, particularly in the form of a system of equations.
Chukwuma Ogbonnaya +3 more
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, 2022 First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are
Alan Baker, David Masser
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Certified Exact Transcendental Real Number Computation in Coq [PDF]
International Conference on Theorem Proving in Higher Order Logics, 2008 Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exactreal number computation.
Russell O’Connor, Russell O’Connor
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Auxiliary functions in transcendental number theory. [PDF]
, 2009 We discuss the role of auxiliary functions in the development of transcendental number theory.Initially, auxiliary functions were completely explicit (Sect. 1). The earliest transcendence proof is due to Liouville (Sect.
Michel Waldschmidt
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