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Does anybody know a closed for
[tex]f(A,B) = \sum_{n\in\mathbb{Z}}e^{-Bn^2 + iAn}[/tex]
with A real and B positive.
[tex]f(A,B) = \sum_{n\in\mathbb{Z}}e^{-Bn^2 + iAn}[/tex]
with A real and B positive.
A closed-form solution is an equation or formula that can be written in a finite number of standard mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation. It is also known as an explicit solution because it explicitly defines the relationship between all variables in the equation.
f(A,B) is a function that represents the relationship between the variables A and B in the closed-form solution equation. The function can be any mathematical operation or combination of operations that produces a value when given specific values for A and B.
Closed-form solutions provide a clear and concise way to express mathematical relationships between variables. They also allow for easy analysis and manipulation of the equation, making it easier to understand and solve complex problems.
A closed-form solution differs from other types of solutions, such as numerical or iterative solutions, in that it provides an exact solution rather than an approximate one. It also allows for direct calculation of the solution, without the need for iterative or trial-and-error methods.
Closed-form solutions are commonly used in physics, engineering, and other scientific fields to model and solve complex systems. They are also used in statistical analysis and data modeling to describe relationships between variables. Additionally, closed-form solutions are often used in computer programming to optimize algorithms and improve computational efficiency.