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  • Author: Praveen Agarwal x
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New Integral Formulas Involving Polynomials and Ī-Function

The aim of the present paper is to evaluate new finite integral formulas involving polynomials and Ī-function. The values of the formulas are obtained in terms of ψ(z) (The logarithmic derivative of Γ(z)). These integral formulas are unified in nature and act as key formula from which we can obtain as their special cases. For the sake of illustration we record here some special cases of our main formulas which are also new and known. The formulas establish here are basic in nature and are likely to find useful applications in the field of science and engineering.


Motivated by resent work of Agarwal [1], the author is establish the new theorem associated with the H - function (Generalized Mellin-Barnes type of Contour Integral), which was introduced and study in a series of papers by by Inayat -Hussain ([12], [13]).Theorem involves a product of the H -function, Generalized hypergeometric functions and Srivastava polynomials. The convergence and existence condition, basic properties of H -function were given by Buschman and Srivastava ([7]). Next, we obtain certain new integrals by the application of our theorem. These results, besides being of very general character have been put in a compact form avoiding the occurrence of infinite series and thus making them useful in applications. Our findings provide interesting unifications and extensions of a number of new results.


Emerging as a new field, quantum computation has reinvented the fundamentals of Computer Science and knowledge theory in a manner consistent with quantum physics. The fact that quantum computation has superior features and new events than classical computation provides benefits in proving mathematical theories. With advances in technology, the nonlinear partial differential equations are used in almost every area, and many difficulties have been overcome by the solutions of these equations. In particular, the complex solutions of KdV and Burgers equations have been shown to be used in modeling a simple turbulence flow. In this study, Burger-like equation with complex solutions is defined in Hilbert space and solved with an example. In addition, these solutions were analyzed. Thanks to the Quantum Burgers-Like equation, the nonlinear differential equation is solved by linearizing. The pattern changes of time made the result linear. This means that the Quantum Burgers-Like equation can be used to smoothen the sonic processing.


Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized (p, q)-Mathieu type series. Then, their composition formulas by using the integral transforms are introduced. Further, a new generalized form of the fractional kinetic equation involving the series is also developed. The solutions of fractional kinetic equations are presented in terms of the Mittag-Leffler function. The results established here are quite general in nature and capable of yielding both known and new results.