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INTEGRATION BY PARTS: AN INTRODUCTION [PDF]
International Journal of Modern Physics A, 2011 Integration by parts is used to reduce scalar Feynman integrals to master integrals.
A. G. GROZIN
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Evaluation of Infinite Series by Integrals
Mathematics, 2022 We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms.
Chunli Li, Wenchang Chu
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On Certain Integrals Related to Saran’s Hypergeometric Function FK
Fractal and Fractional, 2022 In the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function FK, which has applications in specific branches of applied physics and statistics (see below).
Minjie Luo +2 more
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Improper Integrals Involving Powers of Inverse Trigonometric and Hyperbolic Functions
Mathematics, 2022 Three classes of improper integrals involving higher powers of arctanh, arctan, and arcsin are examined using the recursive approach. Numerous explicit formulae are established, which evaluate these integrals in terms of π, ln2, the Riemann zeta function,
Chunli Li, Wenchang Chu
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Вестник Северо-Кавказского федерального университета, 2022 The problems introduced in the article here are the application problems from Mathematics and Engineering Sciences. All presented problems are unabridged and never published problems developed by the author for Pre-Calculus, Calculus and Differential ...
D. D. Gadjiev
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Mathematics, 2021 Segal introduce the Fourier–Wiener transform for the class of polynomial cylinder functions on Hilbert space, and Hida then develop this concept. Negrin define the extended Wiener transform with Hayker et al. In recent papers, Hayker et al. establish the
Hyun Soo Chung
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Higher-order fractional Laplacians: An overview
Bruno Pini Mathematical Analysis Seminar, 2022 We summarize some of the most recent results regarding the theory of higher-order fractional Laplacians, i.e., the operators obtained by considering (non-integer) powers greater than 1 of the Laplace operator.
Nicola Abatangelo
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Formalized Mathematics, 2021 Summary In this article, we deal with Riemann’s improper integral [1], using the Mizar system [2], [3]. Improper integrals with finite values are discussed in [5] by Yamazaki et al., but in general, improper integrals do not assume that they are finite.
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Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation
Axioms, 2022 Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control.
Houssine Zine +3 more
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Sensitivity Analysis Based on Markovian Integration by Parts Formula
Mathematical and Computational Applications, 2017 Sensitivity analysis is widely applied in financial risk management and engineering; it describes the variations brought by the changes of parameters. Since the integration by parts technique for Markov chains is well developed in recent years, in this ...
Yongsheng Hang +4 more
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