Some Identities of the Degenerate Poly-Frobenius-Genocchi Polynomials of Complex Variables

AbstractNumerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation to this, in this paper, we introduce the degenerate poly-Bell polynomials emanating from the degenerate polyexponential functions which are called the poly-Bell polynomials when $\lambda \rightarrow 0$ λ → 0 . Specifically, we demonstrate that they are reduced to the degenerate Bell polynomials if $k = 1$ k = 1 . We also provide explicit representations and combinatorial identities for these polynomials, including Dobinski-like formulas, recurrence relationships, etc.

Download Full-text

Meromorphic or Holomorphic Completion of a Reinhardt Domain

Nagoya Mathematical Journal ◽

10.1017/s0027763000013465 ◽

1970 ◽

Vol 38 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Eiichi Sakai

Keyword(s):

Meromorphic Function ◽

Power Series ◽

Meromorphic Functions ◽

Integral Formula ◽

Complex Variables ◽

Several Complex Variables ◽

Reinhardt Domain ◽

Continuity Theorem ◽

Cauchy’S Integral Formula ◽

Long Time

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.

Download Full-text

Duality and crossing symmetry of the narrow resonance model

Canadian Journal of Physics ◽

10.1139/p70-179 ◽

1970 ◽

Vol 48 (12) ◽

pp. 1426-1429 ◽

Cited By ~ 1

Author(s):

K. Nakazawa

Keyword(s):

Finite Energy ◽

Complex Variables ◽

Narrow Resonance ◽

Veneziano Amplitude ◽

Resonance Model ◽

Sum Rule ◽

Crossing Symmetry ◽

The One

In the narrow resonance approximation, conditions of duality and crossing symmetry are derived using the finite energy sum rule for an amplitude which is completely determined as a function of two complex variables by its meromorphic part in one of these variables. As an example, the one term Veneziano amplitude is discussed.

Download Full-text

Unbalance Response of a Dual Rotor System: Theory and Experiment

Journal of Vibration and Acoustics ◽

10.1115/1.2930368 ◽

1993 ◽

Vol 115 (4) ◽

pp. 427-435 ◽

Cited By ~ 21

Author(s):

K. Gupta ◽

K. D. Gupta ◽

K. Athre

Keyword(s):

System Theory ◽

Transfer Matrix ◽

Mode Shape ◽

Reasonable Agreement ◽

Complex Variables ◽

Rotor System ◽

Experimental Results ◽

Unbalance Response ◽

Theoretical Results ◽

Theory And Experiment

A dual rotor rig is developed and is briefly discussed. The rig is capable of simulating dynamically the two spool aeroengine, though it does not physically resemble the actual aeroengine configuration. Critical speeds, mode shape, and unbalance response are determined experimentally. An extended transfer matrix procedure in complex variables is developed for obtaining unbalance response of dual rotor system. Experimental results obtained are compared with theoretical results and are found to be in reasonable agreement.

Download Full-text