Application of scratchpad to problems in special functions and combinatorics
In this brief survey, we have illustrated some of the uses of computer algebra. It might be objected that our work could well be carried out in almost any computer language; so why bother with SCRATCHPAD? The answer, of course, lies in the naturalness and simplicity of computer algebra approaches to these problems. Expressions like (2.2), (3.1) and (4.1) can be coded in SCRATCHPAD in one line exactly as they are written. They can then be studied with minimal thought about the computer and maximal concentration on what is happening. Often mathematical research consists of sifting low grade ore, and when such sifting requires ingenious programming skills it is likely not to be carried out.
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