Sum of Prabhakar's 3 Param Mittag-Leffler

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In summary: Your Name]In summary, the three parametric Mittag-Leffler function is a generalization of the classical Mittag-Leffler function used in fractional calculus. There are several articles and a book that discuss its properties and applications in various fields. One article by Arshad and Hussain provides a detailed study of the function, while another by Srivastava and Arshad explores its applications. The book "Fractional Calculus and Its Applications" also includes a chapter on the three parametric Mittag-Leffler function.
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I have a series in Prabhakar three parametric mittag-leffler is there any article on that
 
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Hello,

Thank you for your question. I am always interested in exploring new areas of research and learning about different mathematical models. I did some research on the topic you mentioned and found that the three parametric Mittag-Leffler function is a generalization of the classical Mittag-Leffler function, which is commonly used in fractional calculus.

I found a few articles that discuss the three parametric Mittag-Leffler function and its properties. One article, published in the Journal of Mathematical Analysis and Applications, titled "A three-parametric Mittag-Leffler function and its properties," by M. M. Arshad and S. Hussain, provides a detailed study of this function and its applications in fractional calculus.

Another article, published in the journal Fractional Calculus and Applied Analysis, titled "On three parametric Mittag-Leffler function and its applications," by H. Srivastava and M. M. Arshad, discusses the properties and applications of this function in various fields such as physics, engineering, and finance.

I would also recommend checking out the book "Fractional Calculus and Its Applications" by Kenneth S. Miller and Bertram Ross, which includes a chapter on the three parametric Mittag-Leffler function and its properties.

I hope this information helps you in your research. Best of luck with your studies!
 

FAQ: Sum of Prabhakar's 3 Param Mittag-Leffler

What is the Sum of Prabhakar's 3 Param Mittag-Leffler?

The Sum of Prabhakar's 3 Param Mittag-Leffler is a mathematical concept that represents the sum of three Mittag-Leffler functions with different parameters. It is denoted as Eα,β,γ(x) and is defined as the integral of the product of three Mittag-Leffler functions.

How is the Sum of Prabhakar's 3 Param Mittag-Leffler different from the usual Mittag-Leffler function?

The Sum of Prabhakar's 3 Param Mittag-Leffler is a generalization of the usual Mittag-Leffler function. It involves the addition of two extra parameters, β and γ, which allows for more flexibility in the function's shape and behavior. It also has a more complicated integral representation compared to the usual Mittag-Leffler function.

What are the applications of the Sum of Prabhakar's 3 Param Mittag-Leffler?

The Sum of Prabhakar's 3 Param Mittag-Leffler has various applications in physics, engineering, and finance. It is used to model non-exponential relaxation processes, fractional calculus, and anomalous diffusion. It is also used in the analysis of viscoelastic materials, signal processing, and option pricing in financial mathematics.

Is the Sum of Prabhakar's 3 Param Mittag-Leffler a special function?

Yes, the Sum of Prabhakar's 3 Param Mittag-Leffler is considered a special function in mathematics. It falls under the category of Mittag-Leffler type functions, which are a class of special functions that generalize the classical Mittag-Leffler function. These functions have various properties and applications, making them useful in different areas of mathematics and physics.

What are the properties of the Sum of Prabhakar's 3 Param Mittag-Leffler?

The Sum of Prabhakar's 3 Param Mittag-Leffler has many properties, including integral representations, recurrence relations, and asymptotic behavior. It also has a Laplace transform, which can be used to solve differential equations involving this function. Additionally, it has a Taylor series expansion and a Mellin transform, which are useful for its applications in various fields.

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