Mathematics · Special Functions & Differential Equations
A sequence of polynomials Qn(x) [n = 0, 1, 2, ...] satisfies the recursion relation Qn+1(x) - 2xQn(x) + 2nQn-1(x) = 0 for all n ≥ 0 (where Q-1(x) = 0). The generating function for the polynomials, g(x, t) = ∑n=0∞ tnn! Qn(x), satisfies:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1∂g∂t = 2 + (x + t)g
- 2∂g∂t = 2(x - t)t g
- 3∂g∂t = 2(x - t)g✓
- 4∂g∂t = 2(t + x)g
Correct answer
∂g∂t = 2(x - t)g
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