Legendre duplication formula
In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name. The various relations all stem from the same underlying principle; that is, the relation for one special function can be derived from that for the others, and is simply a manifestation of the same identity in different guises.

This is an excerpt from the article Legendre duplication formula from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
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Gamma function - Wikipedia, the free encyclopedia
The notation Γ(t) is due to Legendre. If the real part of the ... \Gamma\left(z + \tfrac{ 1. The duplication formula is a special case of the multiplication theorem.
en.wikipedia.org/wiki/Gamma_function
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Legendre Duplication Formula -- from Wolfram MathWorld
REFERENCES: Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
mathworld.wolfram.com/LegendreDuplicationFormula.html
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Multiplication theorem - Wikipedia, the free encyclopedia
The duplication formula for the gamma function is. \Gamma(z) \; \Gamma\left(z + \ frac. It is also called the Legendre duplication formula or Legendre relation, ...
en.wikipedia.org/wiki/Multiplication_theorem
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Chapter 1. Special Functions > 1.9 - Legendre's Duplication Formula
1.9 Legendre's Duplication Formula. Prove that. images. [JNTU 2003S]. Solution We know beta function as integral of circular functions (B Form VI). images.
my.safaribooksonline.com/book/math/9789332503342/chapter-1dot-special-functions/ch1_sub1_9_xhtml
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Gamma Function - Part 11 - Legendre duplication formula. by MrYouMath • 921 views. Topic: The Legendre duplication formula for the Gamma Function.
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Legendre's Duplication formula Theorem - Math StackExchange
Jul 23, 2013 ... Legendre's Duplication formula Theorem ... k^{x-1}}{(x)_k}$leads immediately to Legendre's duplication formula contained in theorem 1.5.1:. math.stackexchange.com/questions/449537/legendres-duplication-formula-theorem 7 >30 7 Legendre Duplication Formula Legendre duplication formula. Gamma Functions of argument$2z$can be expressed in terms of Gamma Functions of smaller arguments. From the definition of ... archive.lib.msu.edu/crcmath/math/math/l/l168.htm 8 >30 8 Legendre's Duplication Formula - ProofWiki Apr 14, 2013 ... Theorem. Let$\Gamma$denote the gamma function. Then:$\displaystyle \forall z \notin \left\{ -\frac n 2 : n \in \N_0 \right\}, \Gamma \left({z}\right) ...
www.proofwiki.org/wiki/Legendre's_Duplication_Formula
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DUPLICATION FORMULAE FOR THE GAMMA ... - ResearchGate
Mar 26, 2009 ... Legendre's duplication formula for the gamma function ... and hence we obtain Legendre's duplication formula [16, p.240] for the gamma ...
www.researchgate.net/publication/24167180_New_proofs_of_the_duplication_and_multiplication_formulae_for_the_gamma_and_the_Barnes_double_gamma_functions/file/79e4150654ac3a417f.pdf
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Gamma Function - Part 11 - Legendre…
Topic: The Legendre duplication formula for the Gamma Function. What you Should know: - Definition of beta function.
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Legendre duplication formula in science
Gamma function - Wikipedia, the free encyclopedia
The notation Γ(t) is due to Legendre. If the real part of the ... \Gamma\left(z + \tfrac{ 1. The duplication formula is a special case of the multiplication theorem.
Gamma Function -- from Wolfram MathWorld
a slightly unfortunate notation due to Legendre which is now universally used instead of Gauss's simpler Pi(n)=n! (Gauss .... can be expressed using the Legendre duplication formula .... Cambridge, England: Cambridge University Press, 1935.
[PDF]bilateral binomial duplication formula - arXiv.org
Martin Erik Horn, University of Potsdam ... A duplication of the parameters a and c of ..... which can be shown by using Legendre's duplication formula [3, p.22].
[PDF]Victor Namias, A Simple Derivation of Stirling's Asymptotic Series ...
Department of Chemistty and Physics, Purdue University Calumet, Hammond, ... we propose is based on the well-known Legendre duplication formula for the ...
Legendre Duplication Formula -- from Wolfram MathWorld
REFERENCES: Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
Books on the term Legendre duplication formula
Iterative Functional Equations
Marek Kuczma, Bogdan Choczewski, Roman Ger, 1990
For p = 2 equation (10.4.1 1 ) becomes (see (10.4.12')) which is known as Legendre's duplication formula. Moreover, since we have shown in Subsection 10.4C that the 412 Characterization of functions 4D Complex gamma function 4E  ...
Complex Analysis (Undergraduate Texts in Mathematics)
Theodore W. Gamelin, 2003
An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in com...
Irresistible Integrals: Symbolics, Analysis and Experiments ...
George Boros, Victor Moll, 2004
Legendre's Duplication Formula The trigonometric functions satisfy an addition theorem: the relation sin(x + >,) = sin* cosy + siny cos* (10.4.1) and the special case sin 2x = 2 sin x cos x are familiar to the reader. This last result can be written  ...
An Introduction to Partial Differential Equations with MATLAB, Second Edition (Chapman & Hall/CRC Applied Mathematics...
Matthew P. Coleman, 2013
An Introduction to Partial Differential Equations with MATLAB®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat...
Satisficing and Maximizing: Moral Theorists on Practical Reason
Michael Byron, 2004
Legendre's Duplication Formula The trigonometric functions satisfy an addition theorem: the relation sin(x + y) = sin* cosy + siny cos* (10.4.1) and the special case sin 2x = 2 sin x cos x are familiar to the reader. This last result can be written as ...
Mathematical Methods for Physicists, Sixth Edition: A Comprehensive Guide
George B. Arfken, 2005
This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition. * Updates the leading gradu...
Mathematical Methods for Physicists: A Comprehensive Guide
George Brown Arfken, Hans-Jurgen Weber, Frank E. Harris, 2012
Derivation. of. Legendre. Duplication. Formula. The Legendre duplication formula involves products of gamma functions, which suggests that the beta function may provide a useful route to its proof. We start by using Eq. (13.49) forB ( z+ 12 ...
Introduction to Analytic Number Theory (Undergraduate Texts in Mathematics)
1998
"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers....
Scientia Magna international book series (Vol. 8, No. 3, 2012)
editor Zhang Wenpeng
F(z + 1) I z (4) Legendre's duplication formula is defined by: ... +H. 5] r 2 7 Now using Legendre's duplication formula and Recurrence relation for Gamma function, a+b+ (7) r 2 1) Pegarct—l) + more) 2 P] the above formula can be written ...
Partial Differential Equations: An Introduction (Dover Books on Mathematics)
2004
This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. Includes examples of inverse problems arising from improperly posed applications as well as exercis...

Blog posts on the term
Legendre duplication formula
Monday Math 20: The Gamma Function (Part 3/?) | Twisted One 151's Weblog
The Gamma Function Part 3: Beta Function and Legendre duplication: (Part 1) (Part 2) Consider the function defined by . The integral converges for x,y>0; and the substitution in the integral shows that . Now, consider the product of two gamma functions : Now, let us make a change in variables from (u,v) to (r,t)…
twistedone151.wordpress.com/2008/05/19/monday-math-20-the-gamma-function-part-3/
Factoring and Factorials | Gödel's Lost Letter and P=NP
Computing the factorial function fast breaks factoring Adrien-Marie Legendre was one of the great number theorists of the $latex {19^{th}}&fg=000000$ century. He proved a whole host of amazing results. One wonders what he would think of the applications and consequences of his work over a century later. One of his great discovers is the Duplication…
rjlipton.wordpress.com/2009/02/23/factoring-and-factorials/
Duplicating Barnes at E. Kowalski's blog
blogs.ethz.ch/kowalski/2009/09/24/duplicating-barnes/
Spherical Bessel Functions | SouthernMiss Math Archives
Posted on October 1, 2011 by Dr. Lee.
www.math.usm.edu/lee/matharchives/?p=978
Legendre polynomials – orthogonality | Physics pages
Required math: calculus Required physics: none References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education - Problem 4.6. In another post, we found that the Legendre polynomials could be written as an explicit sum as follows $latex \displaystyle P_{n}(x)=\sum_{k=0}^{[n/2]}\frac{(2n-2k)!}{2^{n}(n-k)!k!(n-2k)!}(-1)^{k}x{}^{n-2k} &fg=000000&bg=eedbbd$ This can be written as a derivative if we observe that…
physicspages.com/2011/03/18/legendre-polynomials-orthogonality/
mbt shoes Multiplication theorem – Wikipedia, the | 01mbtschuhe614
Multiplication theorem - Wikipedia,mbt shoes, the free encyclopedia Multiplication theoremFrom Wikipedia,MBT Schuhe, the free encyclopediaJump to: navigation,searchIn mathematics, the multiplication theorem is a certain type of identity obeyed by many ...
34schuhe89.blog.com/2010/06/25/mbt-shoes-multiplication-theorem-wikipedia-the/
William Stein's Number Theory Research Blog: L-functions: a seminar and the Gross-Zagier L-function
Today we had the first meeting of the Advanced Grad Student Number Theory Research Reading Seminar at UW. The participants are me, Robert Miller, Robert Bradshaw, and Craig Citro, and we intend to talk about papers of Dokchitser, Gross-Zagier, Watkins, Delauney, Kartik, Bosman, Kolyvagin, Ghate, and Hida.
389a.blogspot.com/2008/11/l-functions-seminar-and-gross-zagier-l.html
On The Solution -Dimensional of the Composite Operator and Operator
ISRN Applied Mathematics is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of applied mathematics.
www.hindawi.com/isrn/applied.mathematics/2012/952191/
COROLLARY TO EULER´S COROLLARY | PSYCHEDELIC GEOMETRY
It is sure that, after a very short fraction of a second, the first time Euler saw (despite he was one-eyed and partially blind) Gauss´s Gamma Function Multiplication Formula:$latex \displaystyle \prod _{k=0}^{n-1} \Gamma \left(\frac{k}{n}+z\right)=(2 \pi )^{\frac{n-1}{2}} n^{\frac{1}{2}-n z}\Gamma (n z)$Euler tested the expresion with $latex \displaystyle z=\frac{1}{n}$ to get his corollary:\$latex \displaystyle \prod _{k=1}^{n-1} \Gamma…
psychedelicgeometry.wordpress.com/2009/08/27/corollary-to-euler%C2%B4s-corollary/
B.Sc Mathematics Sample Paper for 3rd year Complex Analysis | ItsMyAcademy.com
ItsMyAcademy.com provides various Sample Papers, Papers, Solved Papers, exam tips, project help, exam tips on various subjects like B.Sc, M.Sc, B.A, M.A, BBA, MBA, BCA, B.Com, Fashion Designing, Computers, Science, Chemistry, Biology, Maths, Biochemistry, Graphics, Multimedia, Hospitality, Zoology, Diploma, Post Graduation and all other fields of education