Antenna factor - Revision history

en>Kmarinas86 at 08:29, 20 July 2014

2014-07-20T08:29:10Z

← Older revision		Revision as of 10:29, 20 July 2014
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	~~In [[mathematics]]~~, '''~~Padovan polynomials''' are a generalization of [[Padovan sequence]] numbers. These [[polynomial]]~~s ~~are defined by:~~		I would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my full title. To play domino is something I really appreciate doing. Kentucky is where I've usually been living. Distributing manufacturing is where my main earnings comes from and it's something I truly appreciate.<br><br>my webpage: [http://Myfusionprofits.com/groups/find-out-about-self-improvement-tips-here/ clairvoyance]

	~~:<math>P_n(x)=\left\{\begin{matrix}~~
	~~1,\qquad\qquad\qquad\qquad&\mbox{if }n=1\\~~
	~~0,\qquad\qquad\qquad\qquad&\mbox{if }n=2\\~~
	~~x,\qquad\qquad\qquad\qquad&\mbox{if }n=3\\~~
	~~xP_{n-2}(x)+P_{n-3}(x),&\mbox{if }n\ge4.~~
	~~\end{matrix}\right~~.<~~/math~~>

	~~The first few Padovan polynomials are:~~

	:<~~math~~>~~P_1(x)=1 \,</math>~~
	:~~<math>P_2(x)=0 \,</math>~~
	~~:<math>P_3(x)=x \,</math>~~
	:~~<math>P_4(x)=1 \,<~~/~~math>~~
	~~:<math>P_5(x)=x^2 \,<~~/~~math>~~
	~~:<math>P_6(x)=2x \,<~~/~~math>~~
	~~:<math>P_7(x)=x^3+1 \,<~~/~~math>~~
	~~:<math>P_8(x)=3x^2 \,</math>~~
	~~:<math>P_9(x)=x^4+3x \,</math>~~
	~~:<math>P_{10}(x)=4x^3+1\,</math>~~
	~~:<math>P_{11}(x)=x^5+6x^2.\,</math>~~

	~~The Padovan numbers are recovered by evaluating the polynomials P<sub>''n''~~-~~3</sub>(''x'') at ''x'' = 1.~~

	~~Evaluating P<sub>''n''~~-~~3</sub>(''x'') at ''x'' = 2 gives the ''n''th [[Fibonacci sequence\|Fibonacci number]] plus (~~-~~1)<sup>''n''</sup>. {{OEIS\|id=A008346}}~~

	~~The [[Generating function#Ordinary gnerating function\|ordinary generating function]] for the sequence is~~

	~~:<math> \sum_{n=1}^\infty P_n(x) t^n = \frac{t}{1~~-~~xt^2~~-~~t^3} . <~~/~~math>~~


	~~==See also==~~
	*[[Polynomial sequence]]s

	~~[[Category:Polynomials]~~]

en>Kmarinas86 at 04:51, 16 November 2013

2013-11-16T04:51:37Z

← Older revision		Revision as of 06:51, 16 November 2013
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	~~The title~~ of ~~the writer is Jayson~~. ~~What me and my family members love is performing ballet but I've been taking on new things lately~~. ~~Invoicing is what I do~~. ~~My spouse and I reside in Mississippi and I adore each day living right here~~.<br><br>~~Look~~ at ~~my web page~~ - [~~http:~~/~~/www~~.~~khuplaza~~.~~com~~/~~dent/14869889 best psychic readings~~]		In [[mathematics]], '''Padovan polynomials''' are a generalization of [[Padovan sequence]] numbers. These [[polynomial]]s are defined by:

			:<math>P_n(x)=\left\{\begin{matrix}
			1,\qquad\qquad\qquad\qquad&\mbox{if }n=1\\
			0,\qquad\qquad\qquad\qquad&\mbox{if }n=2\\
			x,\qquad\qquad\qquad\qquad&\mbox{if }n=3\\
			xP_{n-2}(x)+P_{n-3}(x),&\mbox{if }n\ge4.
			\end{matrix}\right.</math>

			The first few Padovan polynomials are:

			:<math>P_1(x)=1 \,</math>
			:<math>P_2(x)=0 \,</math>
			:<math>P_3(x)=x \,</math>
			:<math>P_4(x)=1 \,</math>
			:<math>P_5(x)=x^2 \,</math>
			:<math>P_6(x)=2x \,</math>
			:<math>P_7(x)=x^3+1 \,</math>
			:<math>P_8(x)=3x^2 \,</math>
			:<math>P_9(x)=x^4+3x \,</math>
			:<math>P_{10}(x)=4x^3+1\,</math>
			:<math>P_{11}(x)=x^5+6x^2.\,</math>

			The Padovan numbers are recovered by evaluating the polynomials P<sub>''n''-3</sub>(''x'') at ''x'' = 1.

			Evaluating P<sub>''n''-3</sub>(''x'') at ''x'' = 2 gives the ''n''th [[Fibonacci sequence\|Fibonacci number]] plus (-1)<sup>''n''</sup>. {{OEIS\|id=A008346}}

			The [[Generating function#Ordinary gnerating function\|ordinary generating function]] for the sequence is

			:<math> \sum_{n=1}^\infty P_n(x) t^n = \frac{t}{1-xt^2-t^3} . </math>


			==See also==
			*[[Polynomial sequence]]s

			[[Category:Polynomials]]

en>Pontiga: Corrections of numerical factor in AF and the value of the impedance of free space

2012-04-11T22:33:51Z

Corrections of numerical factor in AF and the value of the impedance of free space

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The title of the writer is Jayson. What me and my family members love is performing ballet but I've been taking on new things lately. Invoicing is what I do. My spouse and I reside in Mississippi and I adore each day living right here.<br><br>Look at my web page - [http://www.khuplaza.com/dent/14869889 best psychic readings]