(1970) Interpolated quadrature formulae containing derivatives for some Cauchy type integrals and for their principal values. Zh. Vychisl. Mat. i Mat. Fiz. 10: pp. 438-444Pykhteev, G. N., Shokamolov, I.: Interpolated quadrature formulae containing derivatives for some Cauchy type integrals and for their principal val...
Integration using substitution is to evaluate integrals and antiderivatives, In this method First we find the assumed variables u and du. Whatever select u to be, du has to be du/dx. Then replace given variables say x and dx by assumed variables u and du. Now know the upper limit and ...
Having two differential equations (1.1) and (1.2) at our disposal, we can demand commu- tativity of the two derivatives. This implies consistency conditions for the two classes of algebra generators involved. We have checked on a case-by-case basis that our realizations of the generators ...
Path Integrals and Exotic Options:. Methods and Numerical Results In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is ...
these formulae allow to trade \(\partial _{y_j}\) derivatives with \(\partial _{m_{j+1}^2}\) derivatives and to treat \(\partial _s\) derivatives. this is useful below when discussing differential equation, integration-by-parts and master integrals for \(\phi _r^d(b_n)\) .|...
We derive a Cauchy–Fantappiè type formula which expresses the derivatives of holomorphic functions at a point on a given analytic variety, in terms of the values of the function in an arbitrarily small neighborhood of the curve which bounds the variety. The formula involves derivatives of ...
Proceedings of the Fifth symposium on fractional differentiation and its applicationsTakeuchi, Y. and Suda, R.: “New numerical computation formula and error analysis of some existing formulae in fractional derivatives and integrals,” The 5th IFAC Symposium on Fraction...
In this way we obtained A˜ as a Q-linear combination of logarithms, for which the correctness of all the partial derivatives was checked analytically. 3.1.2 Simplifying the alphabet The form of A˜ that is found by repeatedly integrating and projecting out components, in the manner of eq...
-family of A-cycle integrals is stable under τ -derivatives and should capture massless n-point one-loop amplitudes of both superstrings and open bosonic strings. The differential-equation setup outlined above will be used to manifest the following prop- erties of open-string α -expansions at...