The equation (1- t 2)y"- 2ty' + a(a + l)y = 0, a constant, is known as the legendre differential equation, and it appears in many areas of mathematics and physics. (a) find 2 linearly independent solutions of the legendre equation. (b) show that the legendre differential equation has a polynomial solution of degree n if a = n. (c) the legendre polynomial pn(t) is defined as the polynomial solution of the legendre equation with a = n which satisfies the condition pn(l) = 1. find p0(t), p1(t), pz(t), and p3(t).

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step-by-step explanati∵∵∴∴on:

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step-by-step explanation:

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!