Meromorphic Functions
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Home > Art, Film & Photography > Meromorphic Functions: Ahlfors Theory, Algebraic Function, Analytic Continuation, Gamma Function, Meromorphic Function, Nevanlinna Theory, Po
Meromorphic Functions: Ahlfors Theory, Algebraic Function, Analytic Continuation, Gamma Function, Meromorphic Function, Nevanlinna Theory, Po

Meromorphic Functions: Ahlfors Theory, Algebraic Function, Analytic Continuation, Gamma Function, Meromorphic Function, Nevanlinna Theory, Po


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 27. Chapters: Ahlfors theory, Algebraic function, Analytic continuation, Gamma function, Meromorphic function, Nevanlinna theory, Pole (complex analysis), Rational function, Removable singularity, Residue (complex analysis), Riemann zeta function, Transcendental function, Value distribution theory of holomorphic functions. Excerpt: In mathematics, the gamma function (represented by the capital Greek letter ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. That is, if n is a positive integer: The gamma function is defined for all complex numbers except the negative integers and zero. For complex numbers with a positive real part, it is defined via an improper integral that converges: This integral function is extended by analytic continuation to all complex numbers except the non-positive integers (where the function has simple poles), yielding the meromorphic function we call the gamma function. The gamma function is a component in various probability-distribution functions, and as such it is applicable in the fields of probability and statistics, as well as combinatorics. It is easy graphically to interpolate the factorial function to non-integer values, but is there a formula that describes the resulting curve?The gamma function can be seen as a solution to the following interpolation problem: "Find a smooth curve that connects the points (x, y) given by y = (x 1)! at the positive integer values for x."A plot of the first few factorials makes clear that such a curve can be drawn, but it would be preferable to have a formula that precisely describes the curve, in which the number of operations does not depend on the size of x. The simple formula for the factorial, n! = 1 x 2 x x n, cannot be used directly for fractional values of x since it is only valid when x is a natural number (i.e., a positive integer). There are, relatively speaking, no such simple solutions for factorials; any combination of sums, products, powers, exponential functions, or logarithms with a fixed number of terms will not suffice to express x!. Stirling's approximation is asymptotically equal to the factorial function for large values of x. It is possible to find a general formula for factorials using tools such as integrals and limits from calculus. A g


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Product Details
  • ISBN-13: 9781156443620
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 28
  • Spine Width: 2 mm
  • Weight: 68 gr
  • ISBN-10: 1156443628
  • Publisher Date: 23 Apr 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Ahlfors Theory, Algebraic Function, Analytic Continuation, Gamma Function, Meromorphic Function, Nevanlinna Theory, Po
  • Width: 189 mm


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