#gamma function

this is the limit approached by iterating the gamma function infinitely. the cyan sections converge on positive real numbers (though i don’t know which) while the black sections diverge. the origin is somewhere between the main bulb and the largest peanut. not pictured: two arms of scaffold-esque geometry extending infinitely up and down to the right, roughly following two curves that i see a lot in my experiments similar to this (infinite tetration, iterated factorial, iteration of z^c+c) but can’t find any meaning to.

In this paper, the generalized gamma functions of the first and second types are firstly introduced and investigated. It can be proven that the traditional gamma function is a special case of the first type of generalized gamma function. Besides, the iterative formula of the generalized gamma function will be fully derived. Finally, a numerical example is provided to illustrate the validity and effectiveness of our main result.