scholarly journals Incremental Linearization for Satisfiability and Verification Modulo Nonlinear Arithmetic and Transcendental Functions

2018 ◽  
Vol 19 (3) ◽  
pp. 1-52 ◽  
Author(s):  
Alessandro Cimatti ◽  
Alberto Griggio ◽  
Ahmed Irfan ◽  
Marco Roveri ◽  
Roberto Sebastiani
Keyword(s):  
Transcendental Functions ◽  
Nonlinear Arithmetic

scholarly journals Simultaneous Contour Method of a Trigonometric Integral by Prudnikov et al.

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1453
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Closed Form ◽  
Contour Method ◽  
Substantial Part ◽  
Exponential Functions ◽  
Closed Form Solutions ◽  
Definite Integrals ◽  
Transcendental Functions ◽  
Trigonometric Integral

In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic and exponential functions. Some of the closed form solutions derived are expressed in terms of elementary or transcendental functions. A substantial part of this work is new.

scholarly journals Pentagon functions for scattering of five massless particles

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
D. Chicherin ◽  
V. Sotnikov
Keyword(s):  
Phase Space ◽  
Numerical Evaluation ◽  
Public Library ◽  
Basis Set ◽  
Particle Scattering ◽  
Minimal Basis ◽  
Feynman Integrals ◽  
Analytic Expressions ◽  
Transcendental Functions ◽  
Branch Cuts

Abstract We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

Maclaurin's type infinite products involving certain transcendental functions

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Mohammad Idris Qureshi ◽  
Mahvish Ali ◽  
Dilshad Ahamad ◽  
Saima Jabee
Keyword(s):  
Infinite Products ◽  
Transcendental Functions
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