Write this Equation using Mathematica

EngWiPy · Jun 29, 2009

Hello everyone,

I have the following equation, and I want to write it using mathematica:

$Equation for M_Z(s) as 2λμ times [I_{λ,μ}(s) - 2 dI_{λ,μ}(s)/ds] plus (λ + μ) times sqrt(λμ) times [J_{λ,μ}(s) - dJ_{λ,μ}(s)/ds], written in LaTeX.$

where:

$Two displayed equations defining I_{\lambda\mu}(s) and J_{\lambda\mu}(s) as ratios involving the Tricomi function Psi(1,1;phi^-(s)), Psi(1,1;phi^+(s)), Psi(1,0;phi^-(s)) and Psi(1,0;phi^+(s)), with denominators containing phi^+(s) minus phi^-(s) and the square root of lambda mu.$

and:

$Equation: phi^{±}_{λ,μ}(s) = (1/2)[s + λ + μ ± sqrt((s + λ + μ)^2 - 4λμ)], with s-subscript λ, μ on the left and the square root term inside the brackets.$

Where [tex]\Psi[/tex] is the tricomi's confluent hypergeometric function, built-in Mathimatica as HypergeometricU[ , , ].
Can anyone help me, please?
Thanks in advance
Best regards

Dale · Jun 30, 2009

I don't understand. What exactly is the difficulty? It seems straightforward, especially since you already know HypergeometricU.

EngWiPy · Jun 30, 2009

DaleSpam said:

I don't understand. What exactly is the difficulty? It seems straightforward, especially since you already know HypergeometricU.

Than you DaleSpam for replying. Actually, I took this equation from a paper which plotted it. When I tried to so do, the program gave may little bit different results, so, I thought that I wrote the program incorrectly using Mathematica. But after I posted this thread, I solved the problem, which was a matter of signs and powers.

Sorry for that, and thanks again.

Regards

Mike^now · Aug 4, 2009

how we can find the law of formation of sequence in mathimatica? pleasezz help.

Dale · Aug 4, 2009

Hi Mike^now, welcome to PF

What does "law of formation of sequence" mean?

Mike^now · Aug 9, 2009

it is a general rule to write a sequence. like 1/2,1/4,1/8/1/16,1/32... has a general rule (1/2^n. where n = number of term.

Dale · Aug 9, 2009

That is not possible to do in general. No matter how many terms you write out, unless you already know the rule, you cannot know the next term.

For example, with the sequence you gave the next number could be 1/32, or the sequence could be cyclic and the next number could be 1/2 again, or it could be a bitshift of a floating point number with 5 bits of precision so that the next term is 0, etc.

Dale · Aug 13, 2009

Hmm, apparently they have a function which tries anyway:
FindSequenceFunction

Mike^now · Aug 30, 2009

This function does not provide general term of sequence ( 4/3,5/4,6/5,7/6...)

By writting FindSequenceFunction[{1, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8}, n] produce as it is. no result.

even i tried sequence starting from 0 as well as from 1 and still it does not produce any formula of general term.

Dale · Sep 1, 2009

Well, that does not surprise me. As I said, it is fundamentally an impossible question. It is pretty impressive that it ever works.

Write this Equation using Mathematica

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