 There is in fact no complex number formula_31 for which formula_179, and hence the reciprocal gamma function formula_180 is an entire function, with zeros at formula_181.The gamma function has a local minimum at (truncated) where it attains the value (truncated).The gamma function must alternate sign between the poles because the product in the forward recurrence contains an odd number of negative factors if the number of poles between formula_31 and formula_164 is odd, and an even number if the number of poles is even.