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K.S. Kölbig, On the zeros of the incomplete gamma functions. This paper is from 1972, it has a whole list of references to older literature.

It is the aim of this note to recall some of the earlier results (occasionally correcting them), and to present a plot containing a few of the zero trajectories of the function $\gamma(xw, x)$ in the complex $w$-plane ($w = u + iv$), as functions of the real parameter $x$ > 0. It will be seen that these trajectories all lie in a finite region of the $w$-plane, and that they cluster towards a limiting curve as shown by Mahler (1930).

This limiting curve is interesting, it is given by $${\rm Re}\,(w\log w-w+1)=0.$$ In the plot below (from Kölbig's paper), you can see how the zeroes approach the limiting curve.

K.S. Kölbig, On the zeros of the incomplete gamma functions. This paper is from 1972, it has a whole list of references to older literature.

It is the aim of this note to recall some of the earlier results (occasionally correcting them), and to present a plot containing a few of the zero trajectories of the function $\gamma(xw, x)$ in the complex $w$-plane ($w = u + iv$), as functions of the real parameter $x$ > 0. It will be seen that these trajectories all lie in a finite region of the $w$-plane, and that they cluster towards a limiting curve as shown by Mahler (1930).

This limiting curve is interesting, it is given by $${\rm Re}\,(w\log w-w+1)=0.$$ In the plot below (from Kölbig's paper), you can see how the zeroes approach the limiting curve.

K.S. Kölbig, On the zeros of the incomplete gamma functions. This paper is from 1972, it has a whole list of references to older literature.

It is the aim of this note to recall some of the earlier results (occasionally correcting them), and to present a plot containing a few of the zero trajectories of the function $\gamma(xw, x)$ in the complex $w$-plane ($w = u + iv$), as functions of the real parameter $x$ > 0. It will be seen that these trajectories all lie in a finite region of the $w$-plane, and that they cluster towards a limiting curve as shown by Mahler (1930).

This limiting curve is interesting, it is given by $${\rm Re}\,(w\log w-w+1)=0.$$

K.S. Kölbig, On the zeros of the incomplete gamma functions. This paper is from 1972, it has a whole list of references to older literature.

It is the aim of this note to recall some of the earlier results (occasionally correcting them), and to present a plot containing a few of the zero trajectories of the function $\gamma(xw, x)$ in the complex $w$-plane ($w = u + iv$), as functions of the real parameter $x$ > 0. It will be seen that these trajectories all lie in a finite region of the $w$-plane, and that they cluster towards a limiting curve as shown by Mahler (1930).

This limiting curve is interesting, it is given by $${\rm Re}\,(w\log w-w+1)=0.$$ In the plot below (from Kölbig's paper), you can see how the zeroes approach the limiting curve.

K.S. Kölbig, On the zeros of the incomplete gamma functions

K.S. Kölbig, On the zeros of the incomplete gamma functions. This paper is from 1972, it has a whole list of references to older literature.

It is the aim of this note to recall some of the earlier results (occasionally correcting them), and to present a plot containing a few of the zero trajectories of the function $\gamma(xw, x)$ in the complex $w$-plane ($w = u + iv$), as functions of the real parameter $x$ > 0. It will be seen that these trajectories all lie in a finite region of the $w$-plane, and that they cluster towards a limiting curve as shown by Mahler (1930).

This limiting curve is interesting, it is given by $${\rm Re}\,(w\log w-w+1)=0.$$