MATHEMATICS - III

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MATHEMATICS - III

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\begin{array}{l} \sum_{r=0}^{n} T_{2 r}(x)=\frac{1}{2}\left(1+\frac{1}{\left(1-x^{2}\right)^{1 / 2}} U_{2 n+1}(x)\right) \\ \text { where, } U_{n}(x)=\sin \left(n \cos ^{-1} x\right) \text { and } T_{n}(x)=\cos \left(n \cos ^{-1} x\right) \end{array}

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Answer 1

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Î 10,19= [1 + U. ()-ce?) V2 ant) con N=0 Ton (0) 11 let a = casia) J=0 n n E Ton (Coso) = Costa Cosicoscov) N=0 n E Coslano)

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MATHEMATICS - III

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MATHEMATICS - III

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Consider the heat conduction problem

Compute the Fourier cosine coefficients for f(x)

Suppose that

Determine whether the series converges or diverges.

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Determine whether the series converges, and if so, find its sum.

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MATHEMATICS - III

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