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Special Functions
In this chapter \(^{1}\) , we shall consider various special...
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Elementary Special Functions
In the field of mathematics, aside from elementary and algebraic functions, there is a large group of special functions. In this chapter, a few of...
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Special Functions
As we have seen in the previous chapters, typically, solutions of differential equations cannot be presented using elementary functions. Generally,...
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Other Special Functions, Supertrigonometric and Superhyperbolic Functions
In this chapter, we propose some other special functions including the Rabotnov fractional exponential function, the Miller–Ross function, the...
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Commonly Used Special Functions: Definitions and Computing
Special functions are dedicated mathematical functions invented by mathematicians. For instance, if the integrand is...
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Loop Integration Techniques and Special Functions
In this chapter we introduce methods for evaluating Feynman loop integrals. We introduce basic methods such as Feynman and Mellin parametrisations,...
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Special Functions in the MPC Formulation
In the LTI-MPC and LTV-MPC formulations discussed in the previous chapters, the number of optimal variables that are to be evaluated at each sampling...
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Integral Transforms and Special Functions
This chapter provides the essential mathematical tools to be used in the subsequent chapters, and is intended to make the book as self-contained as...
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A New Special Class of Ma–Minda Type Starlike Functions
The main objective of this paper is to introduce a new special class of Ma–Minda starlike functions. We find the radii of starlikeness, convexity,...
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Special functions for heat kernel expansion
In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at...
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Special functions emerging from symmetries of the space of solutions to special double confluent Heun equation
A family of quadruplets of interrelated functions holomorphic on the universal cover of the complex plane without zero (for brevity,
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Special classes of isotropic covariance functions
In the literature classical properties concerning the class of covariance functions are well illustrated. A recent analysis has provided the...
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Analysis of Generating Functions for Special Words and Numbers and Algorithms for Computation
Our aim is to construct and compute efficient generating functions enumerating the k -ary Lyndon words having prime number length which arise in many...
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Special Functions in Heat Transfer Problems
The paper investigates the temperature distribution in an infinite cylinder, which is heated by a point heat source or a moving heat source...
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Uniqueness of L functions with special class of meromorphic functions via sharing of pre-image sets
In this article, we address the uniqueness problem of Selberg class L -functions in relation to a question posed in a previous work by Khoai (Ann...
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Definite/Indefinite Integrals Involving Non-integral Powers for Certain Trigonometric Functions Times Special Functions
Treatment of definite integrals possessing non-integral power are mainly presented. Based on definite integrals with integral power(s), non-integral...
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Aggregate special functions to approximate permuting tri-homomorphisms and permuting tri-derivations associated with a tri-additive ψ-functional inequality in Banach algebras
In this paper, we define a new class of control functions through aggregate special functions. These class of control functions help us to stabilize...
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Explicit solution for a Sea-Breeze flow model with special viscosity functions
In this paper, we are concerned with determining the explicit solution of a Sea-Breeze flow model by selecting a special viscosity function. Firstly,...
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Lie Algebra of Special Phase Functions
We review the Lie algebra of special phase functions (see, for instance, [220, 227, 312] and literature therein), along with some improvements and...