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GATE 2022 MA – Question 34

Ordinary Differential Equations · Series Solutions and Special Functions · 1 mark · Numerical answer

Bessel functions satisfy J_(α−1)(x)+J_(α+1)(x)=(2α/x)J_α(x). Find (πJ_(3/2)(π))².

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Correct answer: 2 to 2

Explanation

Use J_(1/2)(x)=√(2/(πx))sin x and J_(−1/2)(x)=√(2/(πx))cos x. At α=1/2, J_(3/2)=J_(1/2)/x−J_(−1/2). At x=π this is √2/π because sinπ=0,cosπ=−1. Thus the square is **2**.

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