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Quantum Engineering Year 0: Mathematical Foundations Month 7Day 194

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Year 0·Month 7·Week 4

Day 194: Special Functions from Complex Analysis

Day 194 of 2,016~5 min read

Learning Objectives

•Define and analyze the Gamma function via complex analysis
•Apply the reflection and duplication formulas
•Understand the Riemann zeta function and analytic continuation
•Compute special values of $\Gamma$ and $\zeta$
•Connect to physics: partition functions, Casimir effect
•Use special functions in quantum calculations

Today's Schedule (7 hours)

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1 The Gamma Function 2 Analytic Continuation of Gamma 3 Reflection Formula 4 The Beta Function 5 The Riemann Zeta Function 6 Analytic Continuation of Zeta 7 Physics Applications

Day 193Day 194 of 2,016Day 195