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#4993 option variable `expand_polynomial` is not documented

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nobody
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5
2026-08-17
2026-08-17
No

The option variable expand_polynomials is defined in hyp.lisp, but it is not documented. The source code says "When NIL do not automatically expand polynomials as a result"

Likely, the option variable should be renamed something like expand_orthogonal_polynomials.

Since the legendre_q functions aren't in general polynomials, it's unclear how expand_polynomials should interact with legendre_q, but I suggest that the following is wrong:

(%i5)   trace(legendre_q);
(%o5)   [legendre_q]
(%i6)   specint(t*bessel_y(0,t)*exp(-t),t), expand_polynomials : false;
1" Simp   "legendre_q[1,psey/sqrt(psey^2+1)]

1" Return "legendre_q(psey*sqrt(psey^2+1)*log((psey/sqrt(psey^2+1)+1)/(1-psey/sqrt(psey^2+1)))-2*psey^2-2)/(2*psey^2+2)

1" Simp   "legendre_q[2,psey/sqrt(psey^2+1)]

1" Return "legendre_q((2*psey^2-1)*log((psey/sqrt(psey^2+1)+1)/(1-psey/sqrt(psey^2+1)))-6*psey*sqrt(psey^2+1))/(4*psey^2+4)

(%o6)   -((sqrt(2)*log((1/sqrt(2)+1)/(1-1/sqrt(2)))-4)/(4*%pi))

The result should be expressed explicitly in terms of the legendre_q function.

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