14.2.2 (a) If Bum is the mth zero of (d/dp) Jy(Bvmp/a), show that the Bessel functions are orthogonal over the interval [0, a] with an orthogonality integral Jv (Bvm²) Jv (Bvn ²) p dp =0, m‡n, v>-1. (b) Derive the corresponding normalization integral (m= n). ANS. 0²/(1-2²) [Jv (Bvm)]², v>-1. vm

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.