Recent content by adpc

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    Bessel type differential equation

    Homework Statement Hello I am trying to solve the following Differential Equation: r^2\frac{d^2R}{dr^2}+r\frac{dR}{dr}-\left[A^2r^4-B^2r^2-C^2]R=0 where A,B and C are constants- Homework Equations I have read this equation is calle "Bessel wave eq" but I can't find the reference...
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    Weierstrass Approximation Theorem

    Homework Statement Show that if f is continuously differentiable on [a, b], then there is a sequence of polynomials pn converging uniformly to f such that p'n converge uniformly to f' as well.Homework Equations The Attempt at a Solution Let pn(t) = cn t^n Use uniform convergence and integrate...
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    Express the indefinite integral as a power series.

    This one doesn't have an antiderivative so you have to express first (exp(x)-1)/x as a Taylor series and then integrate term by term, and you have to make sure that the resultant series converges. You already know the series expansion of exp(x), so it's easy to find the series of exp(x)/x just...
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    Proving Limit of Integral for Nonnegative Continuous Function on [0,1]

    Homework Statement f nonnegative continuous function on the interval [0,1]. Let M be the supremum of f on the interval. Prove: \lim_{n \rightarrow \infty} \left[ \int^1_0 f(t)^n dt \right] ^{1/n} = M Homework Equations The Attempt at a Solution I was trying using Upper Sums but...
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    Prove Integral Inequality: f Nonnegative, Continuous on [0,1]

    Homework Statement For f nonnegative and continuous on [0,1], prove. \left( \int f \right) ^2 < \int f^2 With the limits from 0 to 1. Homework Equations The Attempt at a Solution I was trying to use Upper sums, i.e. \inf \sum \Delta x_i M_i(f^2) = \inf \sum \Delta x_i...
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