human
I wrote the below code

    def replacer(fro, to, factors):
        factors = set(factors)
        def repl(nu, z):
            if factors.intersection(Mul.make_args(z)):
                return to(nu, z)
            return fro(nu, z)
        return repl
    def torewrite(fro, to):
        def tofunc(nu, z):
            return fro(nu, z).rewrite(to)
        return tofunc
    def tominus(fro):
        def tofunc(nu, z):
            return (exp(((I * pi) * nu)) * fro(nu, (exp_polar(((- I) * pi)) * z)))
        return tofunc
    orig_expr = expr
    ifactors = [I, exp_polar(((I * pi) / 2)), exp_polar((((- I) * pi) / 2))]
    expr = expr.replace(besselj, replacer(besselj, torewrite(besselj, besseli), ifactors))
    expr = expr.replace(besseli, replacer(besseli, torewrite(besseli, besselj), ifactors))
    minusfactors = [(-1), exp_polar((I * pi))]
    expr = expr.replace(besselj, replacer(besselj, tominus(besselj), minusfactors))
    expr = expr.replace(besseli, replacer(besseli, tominus(besseli), minusfactors))
    z0 = Dummy('z')
    def expander(fro):
        def repl(nu, z):
            if ((nu % 1) == (S(1) / 2)):
                return exptrigsimp(trigsimp(unpolarify(fro(nu, z0).rewrite(besselj).rewrite(jn).expand(func=True)).subs(z0, z)))
            elif (nu.is_Integer and (nu > 1)):
                return fro(nu, z).expand(func=True)
            return fro(nu, z)
        return repl
    expr = expr.replace(besselj, expander(besselj))
    expr = expr.replace(bessely, expander(bessely))
    expr = expr.replace(besseli, expander(besseli))
    expr = expr.replace(besselk, expander(besselk))
    if (expr != orig_expr):
        expr = expr.factor()
    return expr

What's a good function header?
 ... Here's a good function header?
assistant
#Here's a good function header.

def besselsimp(expr):