The Bureau of Standards Handbook of Mathematical Functions (edited by

Abramowitz and Stegun) provides a host of expressions that are easy to

state, of practical use, and interesting to program. I would suggest it as a

source of problems for discussions of APL programming.

For example, Article 3.6.8 (on page 14 in my edition) states that (1+x) to

the power a can be expressed as the sum of a series using the binomial

coefficients. Moreover, the binomial coefficients are expressed (in 3.6.9)

as quotients with numerators given by the falling factorial function 1, a,

a(a-1), a(a-1)(a-2) ... and with denominators given by the factorials. This

is the form that was used in one or more of the recent messages on the

binomial coefficients.

However, the Handbook continues (3.6.10-14) with the infinite series

obtained for negative and fractional values of the exponent a, showing the

first few values of the numerators and denominators (expressed in lowest

terms). For example, 3.6.12 (with a set to minus one-half) gives the

numerators as 1 _1 3 _5 35 _63 and the denominators as powers of 2.

I would invite APL programs for generating these results for the cases

treated in the Handbook (a set to _1, 1r2, _1r2, 1r3, _1r3). I would

particularly like to see a solution in MATLAB; in spite of the recent flurry

of interest in it, no sample program has appeared.