Lonely

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15 years, 78 days

MaplePrimes Activity


These are questions asked by Lonely

We want to fit

f(x) = a_0 + a_1 *x + a_2 * x^2 + ... + a_n * x^n

to the data (x_i,f(x_i)) for i = 0 ... n.

 

It will give rise to the following system

[ a_i ] = [A]^{-1} * [ f(x_i)].

 

Here [a_i] = [ a_1 a_2 a_3 ... a_n], 

[A] = [ 1 x_0 x_0^2 ... x_0^n ; 1 x_1 x_1^2 ... x_1^n ; 1 x_2 x_2^2 ... x_2^n ; ... ; 1 x_n x_n^2 ... x_n^n]

and 

[f(x_i)] = [f(x_0) f(x_1) f(x_2) ... f(x_n)].

 

i am unable to solve the following inequalities:

ineq1 := (4-(3/2)*q+(1/2)*sqrt(28-24*q+5*q^2))*(1/2-(1/2)*q)

ineq2:=(3-q+(1/4)*sqrt(84-58*q+10*q^2)+(1/4)*sqrt((4-2*q)*(3-q)))*(1/2-(1/2)*q):

 

solve(ineq1<1,q)

 

solve(ineq2<1,q)

 

"Warning, solutions may have been lost"

 

please help me here

 

How may I program the following with Maple?

 

(1) Define the function:

H(p) := p * c1 + p^2 * c2 + p^3 * c3  + ......

 

(2) Now construct the following expression:

 

(1-p) [ v''' + 1 ]  = H(p) [ v''' - 25 * v' + 1]

Here, v is some funciton of x.

 

(3) Now assume: v = u0 + u1 * p + u2 * p^2 + ...

and substitute this into the expression defined at the point (2).

 

Hello Friends,

I have the equation

 

 

I am interested in finding the asymptofic constant (Big O(1/n^(2m+2)) for the following expansion

 

series((1+1/n)^((1/2)/(sum(1/((2*k+1)*(2*n+1)^(2*k+1)), k = 0 .. m))), n = infinity, 10)

 

Upon using the preceding command in the maple i get

 

Error, (in asympt) unable to compute series

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