Most often generating functions arise from recurrence formulas. Sometimes, however, from a generating function you will find a new recurrence formula, not the one you started with, that gives new insights into the nature of your sequence.

Absolute power was forbidden since only gods had the Arguslike wisdom and knowledge that absolute power would necessitate.

Very high purity fused silica glasses are made, which have negligible thermal expansion. Hence, they are suitable for making items of high accuracy such as space telescopes. Photochromatic (also called photochromic) glasses are those glasses that darken in sunlight. These are useful for making cooling glasses.

As we shall see, all of these statements are of limited verity.