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The reciprocal Fibonacci constant ψ is the sum of the reciprocals of the Fibonacci numbers: = = = + + + + + + + +. Because the ratio of successive terms tends to the reciprocal of the golden ratio, which is less than 1, the ratio test shows that the sum converges.
Psi function can refer, in mathematics, to the ordinal collapsing function ...
There is an additive definition of the psi function as well. Quoting from Dickson, [ 1 ] R. Dedekind [ 2 ] proved that, if n {\displaystyle n} is decomposed in every way into a product a b {\displaystyle ab} and if e {\displaystyle e} is the g.c.d. of a , b {\displaystyle a,b} then
Buchholz's psi-functions are a hierarchy of single-argument ordinal functions introduced by German mathematician Wilfried Buchholz in 1986. These functions are a simplified version of the θ {\displaystyle \theta } -functions, but nevertheless have the same strength [ clarification needed ] as those.
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property, using formal methods of mathematics. [1] Formal verification is a key incentive for formal specification of systems, and is at the core of formal methods.
In mathematics, the Fox–Wright function (also known as Fox–Wright Psi function, not to be confused with Wright Omega function) is a generalisation of the generalised hypergeometric function p F q (z) based on ideas of Charles Fox and E. Maitland Wright :
In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose principle is to give names to certain ordinals much larger than the one being defined, perhaps even large cardinals (though they can be replaced with recursively large ordinals at the cost of extra technical ...
the J/psi mesons in particle physics; the stream function in fluid dynamics; the reciprocal Fibonacci constant [29] the second Chebyshev function in number theory [30] the polygamma function in mathematics [31] the supergolden ratio [32] In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm. [33]