Formal Power Series with even or odd terms shouldn't return Piecewise formula for coefficients about sympy

[oscarbenjamin]

It looks like the given form comes from here:

sympy/sympy/series/formal.py

Lines 537 to 561 in 2eb826c

	result = _rsolve_hypergeometric(f, x, P, Q, k, m)
	if result is None:
	return None
	sol_list, ind, mp = result
	sol_dict = defaultdict(lambda: S.Zero)
	for res, cond in sol_list:
	j, mk = cond.as_coeff_Add()
	c = mk.coeff(k)
	if j.is_integer is False:
	res *= x**frac(j)
	j = floor(j)
	res = res.subs(k, (k - j) / c)
	cond = Eq(k % c, j % c)
	sol_dict[cond] += res # Group together formula for same conditions
	sol = []
	for cond, res in sol_dict.items():
	sol.append((res, cond))
	sol.append((S.Zero, True))
	sol = Piecewise(*sol)

Maybe that code or some other code could be a bit smarter about recognising a Piecewise where the expression is zero in one of the cases.

[pierre-haessig]

Thanks for identifying the region. For now I don't have a development setup for SymPy and I guess that understanding the code would be really helped by using a step-by-step debugger.

By the way, is it just me or there are missing doc in rsolve_hypergeometric(f, x, P, Q, k, m): f and x are not documented? Is f(x) the function such that its power series coefficients are the a(n) coefficients mentioned in the docstring?

[oscarbenjamin]

f and x are not documented?

Ideally they would be documented but this is an internal function and not all internal functions have docs.