My first question is: is this formula (at the bottom) a known formula?(adsbygoogle = window.adsbygoogle || []).push({});

In this subject i haven't explained how i build up the formula.

So far i think it is equal to the gamma function of Euler with

[tex] \Gamma\left(\frac{m_1}{m_2}+1\right)= \frac{m_1}{m_2}\ ![/tex]

with

[tex] m_1 , m_2 \in \mathbf{N} [/tex]

and

[tex] 1<m_2 [/tex]

This gamma function however I didn't use.

The next limit i write like L(q,x) in de last formula.

[tex] L(q,x)=\prod^{\infty}_{k=0}\frac{(k+q+x) (k+1)}{(k+q)(k+1+x)}[/tex]

with

[tex] q\neq [/tex]

0,-1,-2,-3, …… and

[tex] x\neq [/tex]

–1,-2,-3,-4, ……..

This is the formula where i use the factorial symbol ! because i think that it gives no problems with arguments with real values.

[tex] \frac{ m_1}{m_2}\ !=\left(m_1\ ! \prod^{ m_2-1}_{ i=1}L\left(1+ i\frac{ m_1}{m_2}, \frac{ m_1}{m_2}\right) \right)^\frac{1}{m_2} [/tex]

with

[tex] m_1 , m_2 \in\mathbf{N} [/tex]

and

[tex] 1<m_2 [/tex]

Please feel free to react.

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# The factorial of a rational number, the gamma function not used

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