Math Problem Statement

How to solve problems related to the Gamma function, Fourier transforms, and the Poisson distribution as shown in the uploaded exam question?

Solution

I see that you've uploaded an image of a mathematical problem. The document appears to be an exam question related to the Gamma function, Fourier transforms, and the Poisson distribution. How can I assist you with this problem? Would you like me to break down any specific part or solve particular questions from it?

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Math Problem Analysis

Mathematical Concepts

Gamma function
Fourier transforms
Poisson distribution
Differential equations
Infinite series convergence

Formulas

Gamma function: Γ(x) = ∫₀⁺∞ t^(x-1)e^(-t) dt
Fourier transform integral: F(x) = ∫₀⁺∞ e^(−t) t^(3/4) e^(ixt) dt
Binomial series expansion
Convergence of power series

Theorems

Properties of the Gamma function
Fourier transform theory
Differential equation techniques for solving F'(x) + A·F(x) = 0

Suitable Grade Level

Undergraduate-level mathematics, typically 2nd or 3rd year