# Continued fractions: analytic theory and applications by William B. Jones

By William B. Jones

This can be an up to date exposition of the analytic idea of endured fractions within the advanced area with emphasis on functions and computational equipment.

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Extra info for Continued fractions: analytic theory and applications

Sample text

There are other ways of doing this, but the basic approach should be evident. The location of the axis of rotation changes slightly with the pendulum’s swing amplitude. If desired, one can determine how much the axis of rotation moves by measuring y at different swing amplitudes, and then plotting y vs the swing amplitude on a graph (see Chapter 5). 20 cha pte r 5 Does a pendulum’s axis of rotation shift with amplitude? 1. Distance of axis of rotation below top end of suspension spring vs swing amplitude.

When the temperature falls, a positive permanent time error occurs. When the temperature rises, a negative permanent time error occurs, so the two errors would appear to cancel, at least partially. The critical issue is whether the permanent time errors cancel completely when the temperature changes in opposite directions at different rates (the usual situation) but with the same total rise and fall in temperature. I do not know yet. My test data is conflicting on this issue, some of it saying yes and some saying no.

1, with the scatter inherently getting larger as the swing amplitude gets smaller. 1 is visually drawn through the center of data scatter, and shows that the axis of rotation does move downward slightly (down the suspension spring), as the pendulum’s swing amplitude increases. 2 0 2 4 6 8 Swing amplitude (deg) (half angle) 10 21 Accurate clock pendulums amplitude increases, but in reality a pendulum actually slows down with increasing amplitude. Apparently there are other bigger factors present.