Has anybody seen this looks kind double Mittag-Leffler

[sarrah1]

Hi
I got stuck with this, it looks like a double mittag-leffler. Has anybody seen it

$$\sum_{k=0}^{\infty}\sum_{j=o}^{\infty} \frac{{t}^ {\alpha (j+k)} {a}^{k} c {b}^{j}} {\varGamma(\alpha j+\alpha k+\alpha+1)} $$

thanks

I wonder why the symbols look so small in the post. the numerator is t raised to alpha(j+k) times a^k times constant c times b^j
thanks
sarrah

 

[Jhoneine]

This is a double Mittag-Leffler function, which is defined as:$$M(t,a,b,\alpha) = \sum_{k=0}^{\infty}\sum_{j=0}^{\infty}\frac{t^{\alpha(j+k)}a^kb^j}{\Gamma(\alpha j+\alpha k+\alpha+1)}.$$This function is used to represent solutions of certain fractional differential equations. It is a generalization of the classical Mittag-Leffler function.

 

[math771]

Hi Sarrah,

I haven't personally seen this specific equation before, but it does look like a double Mittag-Leffler series. The symbols may appear small because they are being displayed in LaTeX, which is a typesetting language commonly used for mathematical equations. It's possible that the person who posted this used a smaller font size for the symbols.

As for the equation itself, it seems to involve a combination of parameters and constants, so it may be difficult to provide a specific interpretation without more context. However, the Mittag-Leffler function is commonly used in mathematical analysis and has applications in various fields such as physics and engineering.

If you need help understanding or solving this equation, I suggest asking for assistance on a math forum or reaching out to a math tutor. Good luck!