VI. The theory of the double gamma function

The present paper continues my researches in the theory of gamma functions. Previously to a certain extent I obtained known results by new methods: none of the succeeding investigations how ever have, I believe, been undertaken or suggested by other mathematicians. In the first paper published in the connection I attempted to give a homogeneous theory of the ordinary gamma function, considered from the point of view of Weierstrass’ function theory. I introduced a parameter ω, and showed that the theory was subordinate to that of a function satisfying the difference equation f(z+ω) - f(z) = z′, s being any complex quantity.