An alternative form for the first-passage probabilities. In the explicit formula (5.7) for the ruin probabilities let

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An alternative form for the first-passage probabilities. In the explicit formula (5.7) for the ruin probabilities let a co. Show that the result is . cos-1x sin x sin xz. dx. Consequently, this formula must be equivalent to (4.14). Verify this by showing that the appropriate difference equations and boundary conditions are satisfied.

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