Digital Library of Mathematical Functions
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8 Incomplete Gamma and Related FunctionsIncomplete Gamma Functions

§8.3 Graphics

Contents

§8.3(i) Real Variables

See accompanying text
Figure 8.3.1: Γ(a,x), a = 0.25, 1, 2, 2.5, 3. Magnify
See accompanying text
Figure 8.3.2: γ(a,x), a = 0.25, 0.5, 0.75, 1. Magnify
See accompanying text
Figure 8.3.3: γ(a,x), a = 1, 2, 2.5, 3. Magnify
See accompanying text
Figure 8.3.4: γ*(a,x) (= x-aP(a,x)), a = 0.25, 0.5, 0.75, 1, 2. Magnify
See accompanying text
Figure 8.3.5: x-a-γ*(a,x) (= x-aQ(a,x)), a = 0.25, 0.5, 1, 2. Magnify
Figure 8.3.6: γ*(a,x) (= x-aP(a,x)), -4x4, -5a4. Magnify

Some monotonicity properties of γ*(a,x) and Γ(a,x) in the four quadrants of the (a,x)-plane in Figure 8.3.6 are given in Erdélyi et al. (1953b, §9.6).

Figure 8.3.7: x-a-γ*(a,x) (= x-aQ(a,x)), 0x4, -5a5. Magnify

§8.3(ii) Complex Argument

In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase. See About Color Map.

Figure 8.3.8: Γ(0.25,x+y), -3x3, -3y3. Principal value. There is a cut along the negative real axis. When x=y=0, Γ(0.25,0)=Γ(0.25)=3.625. Magnify
Figure 8.3.9: γ(0.25,x+y), -3x3, -3y3. Principal value. There is a cut along the negative real axis. Magnify
Figure 8.3.10: γ*(0.25,x+y), -3x3, -3y3. Magnify
Figure 8.3.11: Γ(1,x+y), -3x3, -3y3. Magnify
Figure 8.3.12: γ(1,x+y), -3x3, -3y3. Magnify
Figure 8.3.13: γ*(1,x+y), -3x3, -3y3. Magnify
Figure 8.3.14: Γ(2.5,x+y), -2.2x3, -3y3. Principal value. There is a cut along the negative real axis. When x=y=0, Γ(2.5,0)=Γ(2.5)=1.329. Magnify
Figure 8.3.15: γ(2.5,x+y), -2.2x3, -3y3. Principal value. There is a cut along the negative real axis. Magnify
Figure 8.3.16: γ*(2.5,x+y), -3x3, -3y3. Magnify