Results 21 to 30 of about 92,147 (297)

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

Mathematics, 2021
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.
Robert Reynolds, Allan Stauffer
doaj   +1 more source

Reduction Formulae of 2-refined Neutrosophic Integrals and their Applications [PDF]

Neutrosophic Sets and Systems
The main aim of this manuscript is to establish for the first time the reduction formulae of 2-refined neutrosophic indefinite integrals (shortly, RF2RNII) which have double indeterminacy I1 and I2 respectably.
Florentin Smarandache, Bishnupada Debnath   +1 more
doaj   +1 more source

Calculation of integrals in MathPartner

Discrete and Continuous Models and Applied Computational Science, 2021
We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for ...
Gennadi I. Malaschonok, Alexandr V. Seliverstov   +1 more
doaj   +1 more source

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams [PDF]

, 2017
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in ...
Ablinger, J., Blümlein, J., De Freitas, A., Imamoglu, E., Raab, C. G., Radu, C. -S., Schneider, C., van Hoeij, M.   +7 more
core   +1 more source

The Multivariable Aleph-function involving the Generalized Mellin-Barnes Contour Integrals

Cubo, 2020
In this paper, we have evaluated three definite integrals involving the product of two hypergeometric functions and multivariable Aleph-function. Certain special cases of the main results are also pointed out.
Abdi Oli, Kelelaw Tilahun, G. V. Reddy
doaj   +1 more source

Further Equivalent Binomial Sums

Comptes Rendus. Mathématique, 2021
Five binomial sums are extended by a free parameter $m$, that are shown, through the generating function method, to have the same value. These sums generalize the ones by Ruehr (1980), who discovered them in the study of two unexpected equalities between
Bai, Mei, Chu, Wenchang
doaj   +1 more source

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations [PDF]

, 2017
Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets.
Ablinger, J., Behring, A., Blümlein, J., De Freitas, A., Imamoglu, E., Raab, C. G., Radu, C. -S., Schneider, C., von Manteuffel, M. van Hoeij A.   +8 more
core   +1 more source

Local Identities Involving Jacobi Elliptic Functions [PDF]

, 2003
We derive a number of local identities of arbitrary rank involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with ...
A Khare, A Khare, Arul Lakshminarayan, Avinash Khare, I S Gradshteyn, M Abramowitz, P F Byrd, Uday Sukhatme   +7 more
core   +3 more sources

The method of brackets. Part 2: examples and applications

, 2010
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams.
Gonzalez, Ivan, Moll, Victor H., Straub, Armin   +2 more
core   +1 more source

Definite integrals and operational methods

, 2012
An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type.
Babusci, D., Dattoli, G., Duchamp, G. H. E., Górska, K., Penson, K. A.   +4 more
core   +1 more source