Debye asymptotic for Legendre polynomials

For fixed

0 < θ < π

,

P_{n} (cos θ) \sim \frac{2}{πn s i n θ} cos ((n + \frac{1}{2}) θ - \frac{π}{4}) .

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- Hyperbolic Debye asymptotic for Legendre polynomials Debye asymptotic for Legendre polynomials

Hyperbolic Debye asymptotic for Legendre polynomials

For fixed

ξ > 0

,

P_{n} (cosh ξ) \sim \frac{e ^{(n + 1/2) ξ}}{2 πn s i n h ξ} .

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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 30D / b / iii / Solution
Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 336 / 1 / 1 / Solution

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