Symmetric Function G(x,s) and Linear Operator L: A Guide to Solving Equations

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  • #1
eljose
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let be the symmetric function

[tex] G(x,s)=\frac{1}{exp(sx)-1} [/tex]

then get the linear operator L so [tex]LG(x,s)=\delta(x-s) [/tex]
 
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  • #2
so what's the problem, i don't understand what u want
 
  • #3
mathmike said:
so what's the problem, i don't understand what u want
Looks like what is wanted is what operator has G as it green function.
 
  • #4
Yew that,s precisely what i want to know, for a G (green function given) calculate the operator that it satisfies
 

1. What is a symmetric function?

A symmetric function is a mathematical function that remains unchanged when its variables are interchanged. This means that if you swap the values of the variables, the function will still give the same output.

2. How is G(x,s) used in solving equations?

G(x,s) is used as a transformation function in solving equations. It transforms the original equation into a simpler form that is easier to solve. This simplification is achieved by using the properties of symmetry to eliminate variables or reduce the complexity of the equation.

3. What is the role of Linear Operator L in solving equations?

Linear Operator L is used to represent the operations that are performed on the equation. It helps to manipulate the equation and transform it into a simpler form. This simplification is crucial in finding solutions to the equation.

4. Can G(x,s) and L be used to solve all types of equations?

Yes, G(x,s) and L can be used to solve a wide range of equations, including linear, quadratic, and polynomial equations. However, the effectiveness of these methods may vary depending on the complexity of the equation.

5. Are there any limitations to using Symmetric Function G(x,s) and Linear Operator L for solving equations?

One limitation of using these methods is that they may not be suitable for solving nonlinear equations. In addition, the transformation process may result in loss of information, making it challenging to find the exact solution. Therefore, it is essential to consider the nature of the equation before using these methods for solving it.

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