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Infinite Compositions Of Analytic Functions
In mathematics, infinite Function composition, compositions of analytic functions (ICAF) offer alternative formulations of Generalized continued fraction, analytic continued fractions, series (mathematics), series, product (mathematics), products and other infinite expansions, and the theory evolving from such compositions may shed light on the convergence (mathematics), convergence/divergence of these expansions. Some functions can actually be expanded directly as infinite compositions. In addition, it is possible to use ICAF to evaluate solutions of fixed point (mathematics), fixed point equations involving infinite expansions. Complex dynamics offers another venue for iterated function system, iteration of systems of functions rather than a single function. For infinite compositions of a ''single function'' see Iterated function. For compositions of a finite number of functions, useful in fractal theory, see Iterated function system. Although the title of this article specifies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Function Composition
In mathematics, the composition operator \circ takes two function (mathematics), functions, f and g, and returns a new function h(x) := (g \circ f) (x) = g(f(x)). Thus, the function is function application, applied after applying to . (g \circ f) is pronounced "the composition of and ". Reverse composition, sometimes denoted f \mapsto g , applies the operation in the opposite order, applying f first and g second. Intuitively, reverse composition is a chaining process in which the output of function feeds the input of function . The composition of functions is a special case of the composition of relations, sometimes also denoted by \circ. As a result, all properties of composition of relations are true of composition of functions, such as #Properties, associativity. Examples * Composition of functions on a finite set (mathematics), set: If , and , then , as shown in the figure. * Composition of functions on an infinite set: If (where is the set of all real numbers) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Continued Fraction1
''...Continued'' is the second album released by Tony Joe White. It was released on Monument Records and contained the single "Roosevelt and Ira Lee" It was recorded at Monument Studios, Nashville and Lyn-Lou Studios, Memphis in 1969. It was produced by Billy Swan and engineered by Tommy Strong and Mort Thomasson. The album was re-released on by Movieplay/Intermusic from Portugal in 1993 with a different cover and another title (''Roosevelt And Ira Lee''). In 1997 it was rereleased by Warner Brothers containing two additional songs - "Watching The Trains Go By" (by Dewey Oldham and Wallace Pennington) and "Old Man Willis" (by Tony Joe White himself) was the second single. "Old Man Willis" was later re-recorded for the album. The album contained the track "Rainy Night In Georgia" popularized by R&B vocalist Brook Benton in 1970. It reached #4 on the Pop Singles and #2 on the Adult Contemporary charts, respectively. The RIAA certified the single gold for sales of one million c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
