Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: how to find a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105221] Re: how to find a function
  • From: dh <dh at metrohm.com>
  • Date: Wed, 25 Nov 2009 02:29:48 -0500 (EST)
  • References: <hegehq$17j$1@smc.vnet.net>


barefoot gigantor wrote:

> Dear Math Group:-

> 

> Suppose we have:-

> 

> x = a * e  + (2*b - 3*a^2) * e^2

> 

> Now let us find such functions:

> 

> F(x) = 1 + a * e + (2 * b - a^2) * e^2 + ......

> 

> we are just interested in the first three terms.

> 

> Now two such functions can be:

> 

> F1(x) =  1 + x + 2 * x^2

> 

> and

> 

> F2(x) = (1-x)/(1-2*x)

> 

> How can we find all such functions F(x)?

> 

Hi,

all such function can be written as:

F[x]== 1 + a * e + (2 * b - a^2) * e^2 + e^3 PS[e]

where PS[e] is a power series (terminating or not, converging in a 

circle) in e.

To get an expression in x we may solve x for for e:

sol=Solve[x==a * e  + (2*b - 3*a^2) * e^2, e]

we may use these solutions above to get F[x] in terms of x. PS[e] can 

then be replaced by any analytic function of x.

E.g. one possibility:

F[x]=1 + (a (a - Sqrt[a^2 - 12 a^2 x + 8 b x]))/(

  2 (3 a^2 - 2 b)) + ((-a^2 + 2 b) (a - Sqrt[

     a^2 - 12 a^2 x + 8 b x])^2)/(4 (3 a^2 - 2 b)^2) + (

  fun (a - Sqrt[a^2 - 12 a^2 x + 8 b x])^3)/(8 (3 a^2 - 2 b)^3)

where fun is a function of x.



Daniel




  • Prev by Date: Silent errors in Mathematica options, I think it should be detected.
  • Next by Date: Re: how to read in a number in hex and convert it to binary
  • Previous by thread: how to find a function
  • Next by thread: Bug in Plot3D?