What is the significance of the semicolon in function notation?

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In summary, the semicolon in the notation for a function like G(r1, r2; z) is used to separate variables from parameters. In the context of the examples provided, z is a complex parameter that is chosen to be a specific value and does not vary within the function, while r1 and r2 are variables in the Green's function. This can be compared to the difference between constants and variables in computer programming. The original sources for this information are Equation 3.1 in the paper "On the Green's Function for a Finite Domain" and the expression ##\phi(x; E)## in the lecture notes for Quantum Physics I.
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Swamp Thing
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What does the semicolon mean in the notation for a function like G(r1, r2; z) ?
 
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In what context is this ? Can you link to the original source ?
 
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I think ( though not 100% sure ) that the semicolon is used in these examples to separate variables from parameters; for example, in G(r1,r2;z), the z is a complex parameter which you choose to be of a specific value ( and which doesn't vary within the function ), whereas r1 and r2 are actual variables in the Green's function. If we were talking about computer programming, this would be analogous to the difference between constants and variables.

Let's wait for one of the experts here to confirm or correct this, though.
 
  • #5
Thanks !
 

Related to What is the significance of the semicolon in function notation?

1. What does "G(r1, r2 ; z)" notation represent?

The "G(r1, r2 ; z)" notation represents a function, where r1 and r2 are variables and z is a parameter. This notation is commonly used in mathematics and physics to denote a function with multiple variables and parameters.

2. How do you interpret the variables and parameters in "G(r1, r2 ; z)"?

The variables, r1 and r2, represent the independent variables of the function, while the parameter, z, represents a constant or dependent variable. The specific interpretation of these variables and parameters will depend on the context in which the notation is being used.

3. Can you give an example of a function represented by "G(r1, r2 ; z)"?

One example of a function represented by "G(r1, r2 ; z)" is the Green's function, which is used to solve differential equations in physics. In this context, r1 and r2 could represent the positions of two particles, while z represents a parameter such as time or energy.

4. How is "G(r1, r2 ; z)" notation different from other notations for functions?

The "G(r1, r2 ; z)" notation is different from other notations for functions in that it explicitly shows the variables and parameters of the function. Other notations, such as f(x) or y = mx + b, may not indicate the specific variables and parameters being used in the function.

5. What are the benefits of using "G(r1, r2 ; z)" notation?

Using "G(r1, r2 ; z)" notation can make it easier to understand and manipulate functions with multiple variables and parameters. It also allows for consistency and clarity when communicating mathematical concepts and equations.

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