Airy functionsVolterra functiondiffusion equationlinearized Korteweg-de Vries equationIn this short paper, we give some integrals involving Volterra mu-functions and Airy functions. In particular, we prove that Volterra functions behave as eigenfunctions of integral equations whose kernels are solutions of ...
In this paper, using the method of the generating function, we evaluate three different types of integrals involving generalized Bessel functions. Some particular cases are also obtaineddoi:10.1080/10652460108819349Leda GaluéCentro de Investigación de Matemática Aplicada (C.I.M.A.) , Facultad de ...
View Solution Integration of some particular functions View Solution Application Of Integration|Some Standard Graph Of Quadratic Equation View Solution Recommended Questions Manipulating Integrals || Some Special Integrals 57:03 Some important formulas of integration 05:11 SPECIAL INTEGRAL 41:38 SPECIAL INT...
Some third of the material is concerned with biographical and other contextual issues, while the bulk of the selections focus on particular aspects of Euler's contributions to mathematics, including infinite series, the zeta functions, Euler's constant, differentials, multiple integrals, the calculus ...
In particular, the following equality is valid for all values of a, b, and c: (ab)c = ab·c. If f and g are standard mathematical functions and f(g(x)) = x for all small positive numbers, then f(g(x)) = x is assumed to be valid for all complex values x. In particular:...
1.3. Particles and particular partitions The FEP is concerned with self-organisation, which calls for an individuation of ‘self’ from nonself. We consider a particular partition of (generalised) states necessary to separate the internal states of something (i.e., a particle) from its external...
In this paper, the authors study monotonicity and convexity of the generalized elliptic integrals and certain combinations of these special functions, such as ma(r) and μa(r). Making use of these results, the authors obtain some sharp inequalities for the so-called Ramanujan's generalized modul...
As a test case for this work, we study a particular class of Feynman integrals: the one-loop “triangle” Feynman integrals, (2.1) which correspond to the Feynman graph shown in Fig.1. These integrals are relevant to describe the scattering of three particles with momenta(withdue to momentum...
So Sˆ ∈ L2, which was used in the proof of Lemma 1. 3.2 Hyperbolic-cosine function Similarly as in Section 3.1 for the hyperbolic-sine functions, for the hyperbolic-cosine function, we have the following: Some definite integrals arising from selfdecomposable characteristic functions 295 Lemma...
Much of the subject matter in Wan's dissertation [20] is closely related to some of our main techniques. One of our key methods is the manipulation of generating functions for Legendre polynomials to construct new rational approximations for 1π, as is the case with [20]. The section in ...