New properties of the Lerch's transcendent

Abstract

A new representation of the Lerch's transcendent Phi(z,s,a), valid for positive integer s=n=1,2,... and for z and a belonging to certain regions of the complex plane, is presented. It allows to write an equation relating Phi(z,n,a) and Phi(1/z,n,1-a), which provides an expansion of Phi(z,n,a) as a power series of 1/z, convergent for |z|>1.

11 pages, 1 figure

References in corpus (3)

• Representation of Integral Dispersion Relations by Local Forms
• The Lerch zeta function III. Polylogarithms and special values
• Two-point derivative dispersion relations

Cited by in corpus (7)

• Sinc approximation of algebraically decaying functions
• Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness
• The Bandwagon Effect: Not Just Another Bias
• Structure of Forward pp and pp Elastic Amplitudes at Low Energies
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Twisted logarithmic modules of lattice vertex algebras
• Exact treatment of dispersion relations in pp and pp elastic scattering