Logarithmic derivative of an entire function

A property of the derivative of an entire function

We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set. MSC 2010: 30D30.

Ramanujan's Formula for the Logarithmic Derivative of the Gamma Function

Abstract. We prove a remarkable formula of Ramanujan for the logarithmic derivative of the gamma function, which converges more rapidly than classical expansions, and which is stated without proof in the notebooks [5]. The formula has a number of very interesting consequences which we derive, including an elegant hyperbolic summation, Ramanujan’s formula for the Riemann zeta function evaluated ...

Modulus and Phase of the Reduced Logarithmic Derivative of the Hankel Function

The modulus and phase of the reduced logarithmic derivative of the Hankel function zH^'iz)/Hi'\z) for complex variable z and real order v, are investigated. Special attention is paid to the location of saddle points and their trajectories as v varies.

On Relations among Some Constants of an Entire Function

If Piz) is an entire function of order p, it is known that (1) M, m are its type and co-type, in case/ happens to be the rank (or position) function of the maximum term of the Maclaurin series of P (see Chapter II of [l] and Chapter II of [2]) and that (2) M and m are the logarithmic type and co-type of P, if fix) is the number of zeroes z of Piz) such that \z\ ^x (see Jensen's Theorem, Chapter...

Sums of an Entire Function in Certain Weighted L-spaces