Incomplete Gamma and Related Functions - 8.6 Integral Representations

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
8.6.E1 γ ⁡ ( a , z ) = z a sin ⁡ ( π ⁢ a ) ⁢ ∫ 0 π e z ⁢ cos ⁡ t ⁢ cos ⁡ ( a ⁢ t + z ⁢ sin ⁡ t ) ⁢ d t incomplete-gamma 𝑎 𝑧 superscript 𝑧 𝑎 𝜋 𝑎 superscript subscript 0 𝜋 superscript 𝑒 𝑧 𝑡 𝑎 𝑡 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{z^{a}}{\sin\left(\pi a% \right)}\int_{0}^{\pi}e^{z\cos t}\cos\left(at+z\sin t\right)\mathrm{d}t}}
\incgamma@{a}{z} = \frac{z^{a}}{\sin@{\pi a}}\int_{0}^{\pi}e^{z\cos@@{t}}\cos@{at+z\sin@@{t}}\diff{t}		 ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}} 
GAMMA(a)-GAMMA(a, z) = ((z)^(a))/(sin(Pi*a))*int(exp(z*cos(t))*cos(a*t + z*sin(t)), t = 0..Pi)

Gamma[a, 0, z] == Divide[(z)^(a),Sin[Pi*a]]*Integrate[Exp[z*Cos[t]]*Cos[a*t + z*Sin[t]], {t, 0, Pi}, GenerateConditions->None]
Failure Aborted
Failed [14 / 21]
Result: 1.922649672+.1964472815*I
Test Values: {a = .5, z = 1/2*3^(1/2)+1/2*I, a = 3/2}


Result: 2.511118576+1.941926371*I
Test Values: {a = .5, z = -1/2+1/2*I*3^(1/2), a = 3/2}

... skip entries to safe data
 Skipped - Because timed out
8.6.E2 γ ⁡ ( a , z ) = z 1 2 ⁢ a ⁢ ∫ 0 ∞ e - t ⁢ t 1 2 ⁢ a - 1 ⁢ J a ⁡ ( 2 ⁢ z ⁢ t ) ⁢ d t incomplete-gamma 𝑎 𝑧 superscript 𝑧 1 2 𝑎 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 1 2 𝑎 1 Bessel-J 𝑎 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=z^{\frac{1}{2}a}\int_{0}^{% \infty}e^{-t}t^{\frac{1}{2}a-1}J_{a}\left(2\sqrt{zt}\right)\mathrm{d}t}}
\incgamma@{a}{z} = z^{\frac{1}{2}a}\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}a-1}\BesselJ{a}@{2\sqrt{zt}}\diff{t}		 ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}} 
GAMMA(a)-GAMMA(a, z) = (z)^((1)/(2)*a)* int(exp(- t)*(t)^((1)/(2)*a - 1)* BesselJ(a, 2*sqrt(z*t)), t = 0..infinity)

Gamma[a, 0, z] == (z)^(Divide[1,2]*a)* Integrate[Exp[- t]*(t)^(Divide[1,2]*a - 1)* BesselJ[a, 2*Sqrt[z*t]], {t, 0, Infinity}, GenerateConditions->None]
Failure Aborted Successful [Tested: 21] Skipped - Because timed out
8.6.E3 γ ⁡ ( a , z ) = z a ⁢ ∫ 0 ∞ exp ⁡ ( - a ⁢ t - z ⁢ e - t ) ⁢ d t incomplete-gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript subscript 0 𝑎 𝑡 𝑧 superscript 𝑒 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=z^{a}\int_{0}^{\infty}\exp% \left(-at-ze^{-t}\right)\mathrm{d}t}}
\incgamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{-at-ze^{-t}}\diff{t}		 ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}} 
GAMMA(a)-GAMMA(a, z) = (z)^(a)* int(exp(- a*t - z*exp(- t)), t = 0..infinity)

Gamma[a, 0, z] == (z)^(a)* Integrate[Exp[- a*t - z*Exp[- t]], {t, 0, Infinity}, GenerateConditions->None]
Failure Successful Successful [Tested: 21] Successful [Tested: 21]
8.6.E4 Γ ⁡ ( a , z ) = z a ⁢ e - z Γ ⁡ ( 1 - a ) ⁢ ∫ 0 ∞ t - a ⁢ e - t z + t ⁢ d t incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑡 𝑎 superscript 𝑒 𝑡 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{z^{a}e^{-z}}{\Gamma% \left(1-a\right)}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\mathrm{d}t}}
\incGamma@{a}{z} = \frac{z^{a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\diff{t}		 | ph ⁡ z | < π , ℜ ⁡ a < 1 , ℜ ⁡ ( 1 - a ) > 0 formulae-sequence phase 𝑧 𝜋 formulae-sequence 𝑎 1 1 𝑎 0 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi,\Re a<1,\Re(1-a)>0}} 
GAMMA(a, z) = ((z)^(a)* exp(- z))/(GAMMA(1 - a))*int(((t)^(- a)* exp(- t))/(z + t), t = 0..infinity)

Gamma[a, z] == Divide[(z)^(a)* Exp[- z],Gamma[1 - a]]*Integrate[Divide[(t)^(- a)* Exp[- t],z + t], {t, 0, Infinity}, GenerateConditions->None]
Failure Successful
Failed [12 / 28]
Result: Float(infinity)+Float(infinity)*I
Test Values: {a = -1.5, z = 1/2*3^(1/2)+1/2*I}


Result: Float(infinity)+Float(infinity)*I
Test Values: {a = -1.5, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
 Successful [Tested: 28]
8.6.E5 Γ ⁡ ( a , z ) = z a ⁢ e - z ⁢ ∫ 0 ∞ e - z ⁢ t ( 1 + t ) 1 - a ⁢ d t incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 1 𝑡 1 𝑎 𝑡 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=z^{a}e^{-z}\int_{0}^{\infty% }\frac{e^{-zt}}{(1+t)^{1-a}}\mathrm{d}t}}
\incGamma@{a}{z} = z^{a}e^{-z}\int_{0}^{\infty}\frac{e^{-zt}}{(1+t)^{1-a}}\diff{t}		 ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}} 
GAMMA(a, z) = (z)^(a)* exp(- z)*int((exp(- z*t))/((1 + t)^(1 - a)), t = 0..infinity)

Gamma[a, z] == (z)^(a)* Exp[- z]*Integrate[Divide[Exp[- z*t],(1 + t)^(1 - a)], {t, 0, Infinity}, GenerateConditions->None]
Successful Successful - Successful [Tested: 30]
8.6.E6 Γ ⁡ ( a , z ) = 2 ⁢ z 1 2 ⁢ a ⁢ e - z Γ ⁡ ( 1 - a ) ⁢ ∫ 0 ∞ e - t ⁢ t - 1 2 ⁢ a ⁢ K a ⁡ ( 2 ⁢ z ⁢ t ) ⁢ d t incomplete-Gamma 𝑎 𝑧 2 superscript 𝑧 1 2 𝑎 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 1 2 𝑎 modified-Bessel-second-kind 𝑎 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{2z^{\frac{1}{2}a}e^{-% z}}{\Gamma\left(1-a\right)}\int_{0}^{\infty}e^{-t}t^{-\frac{1}{2}a}K_{a}\left(% 2\sqrt{zt}\right)\mathrm{d}t}}
\incGamma@{a}{z} = \frac{2z^{\frac{1}{2}a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}e^{-t}t^{-\frac{1}{2}a}\modBesselK{a}@{2\sqrt{zt}}\diff{t}		 ℜ ⁡ a < 1 , ℜ ⁡ ( 1 - a ) > 0 formulae-sequence 𝑎 1 1 𝑎 0 {\displaystyle{\displaystyle\Re a<1,\Re(1-a)>0}} 
GAMMA(a, z) = (2*(z)^((1)/(2)*a)* exp(- z))/(GAMMA(1 - a))*int(exp(- t)*(t)^(-(1)/(2)*a)* BesselK(a, 2*sqrt(z*t)), t = 0..infinity)

Gamma[a, z] == Divide[2*(z)^(Divide[1,2]*a)* Exp[- z],Gamma[1 - a]]*Integrate[Exp[- t]*(t)^(-Divide[1,2]*a)* BesselK[a, 2*Sqrt[z*t]], {t, 0, Infinity}, GenerateConditions->None]
Successful Aborted - Successful [Tested: 28]
8.6.E7 Γ ⁡ ( a , z ) = z a ⁢ ∫ 0 ∞ exp ⁡ ( a ⁢ t - z ⁢ e t ) ⁢ d t incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript subscript 0 𝑎 𝑡 𝑧 superscript 𝑒 𝑡 𝑡 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=z^{a}\int_{0}^{\infty}\exp% \left(at-ze^{t}\right)\mathrm{d}t}}
\incGamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{at-ze^{t}}\diff{t}		 ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}} 
GAMMA(a, z) = (z)^(a)* int(exp(a*t - z*exp(t)), t = 0..infinity)

Gamma[a, z] == (z)^(a)* Integrate[Exp[a*t - z*Exp[t]], {t, 0, Infinity}, GenerateConditions->None]
Failure Successful Successful [Tested: 30] Successful [Tested: 30]
8.6.E8 γ ⁡ ( a , z ) = - i ⁢ z a 2 ⁢ sin ⁡ ( π ⁢ a ) ⁢ ∫ - 1 ( 0 + ) t a - 1 ⁢ e z ⁢ t ⁢ d t incomplete-gamma 𝑎 𝑧 imaginary-unit superscript 𝑧 𝑎 2 𝜋 𝑎 superscript subscript 1 limit-from 0 superscript 𝑡 𝑎 1 superscript 𝑒 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{-\mathrm{i}z^{a}}{2% \sin\left(\pi a\right)}\int_{-1}^{(0+)}t^{a-1}e^{zt}\mathrm{d}t}}
\incgamma@{a}{z} = \frac{-\iunit z^{a}}{2\sin@{\pi a}}\int_{-1}^{(0+)}t^{a-1}e^{zt}\diff{t}		 z ≠ 0 , ℜ ⁡ a > 0 formulae-sequence 𝑧 0 𝑎 0 {\displaystyle{\displaystyle z\neq 0,\Re a>0}} 
GAMMA(a)-GAMMA(a, z) = (- I*(z)^(a))/(2*sin(Pi*a))*int((t)^(a - 1)* exp(z*t), t = - 1..(0 +))

Gamma[a, 0, z] == Divide[- I*(z)^(a),2*Sin[Pi*a]]*Integrate[(t)^(a - 1)* Exp[z*t], {t, - 1, (0 +)}, GenerateConditions->None]
Error Failure - Error
8.6.E9 Γ ⁡ ( - a , z ⁢ e + π ⁢ i ) = e z ⁢ e - π ⁢ i ⁢ a Γ ⁡ ( 1 + a ) ⁢ ∫ 0 ∞ t a ⁢ e - z ⁢ t t - 1 ⁢ d t incomplete-Gamma 𝑎 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑒 𝑧 superscript 𝑒 𝜋 imaginary-unit 𝑎 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑡 𝑎 superscript 𝑒 𝑧 𝑡 𝑡 1 𝑡 {\displaystyle{\displaystyle\Gamma\left(-a,ze^{+\pi i}\right)=\frac{e^{z}e^{-% \pi\mathrm{i}a}}{\Gamma\left(1+a\right)}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t% -1}\mathrm{d}t}}
\incGamma@{-a}{ze^{+\pi i}} = \frac{e^{z}e^{-\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}		 ℜ ⁡ z > 0 , ℜ ⁡ a > - 1 , ℜ ⁡ ( 1 + a ) > 0 formulae-sequence 𝑧 0 formulae-sequence 𝑎 1 1 𝑎 0 {\displaystyle{\displaystyle\Re z>0,\Re a>-1,\Re(1+a)>0}} 
GAMMA(- a, z*exp(+ Pi*I)) = (exp(z)*exp(- Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity)

Gamma[- a, z*Exp[+ Pi*I]] == Divide[Exp[z]*Exp[- Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}, GenerateConditions->None]
Failure Aborted
Failed [20 / 20]
Result: Float(infinity)+Float(infinity)*I
Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I}


Result: Float(infinity)+Float(infinity)*I
Test Values: {a = 1.5, z = 1/2-1/2*I*3^(1/2)}

... skip entries to safe data
 Skipped - Because timed out
8.6.E9 Γ ⁡ ( - a , z ⁢ e - π ⁢ i ) = e z ⁢ e + π ⁢ i ⁢ a Γ ⁡ ( 1 + a ) ⁢ ∫ 0 ∞ t a ⁢ e - z ⁢ t t - 1 ⁢ d t incomplete-Gamma 𝑎 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑒 𝑧 superscript 𝑒 𝜋 imaginary-unit 𝑎 Euler-Gamma 1 𝑎 superscript subscript 0 superscript 𝑡 𝑎 superscript 𝑒 𝑧 𝑡 𝑡 1 𝑡 {\displaystyle{\displaystyle\Gamma\left(-a,ze^{-\pi i}\right)=\frac{e^{z}e^{+% \pi\mathrm{i}a}}{\Gamma\left(1+a\right)}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t% -1}\mathrm{d}t}}
\incGamma@{-a}{ze^{-\pi i}} = \frac{e^{z}e^{+\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}		 ℜ ⁡ z > 0 , ℜ ⁡ a > - 1 , ℜ ⁡ ( 1 + a ) > 0 formulae-sequence 𝑧 0 formulae-sequence 𝑎 1 1 𝑎 0 {\displaystyle{\displaystyle\Re z>0,\Re a>-1,\Re(1+a)>0}} 
GAMMA(- a, z*exp(- Pi*I)) = (exp(z)*exp(+ Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity)

Gamma[- a, z*Exp[- Pi*I]] == Divide[Exp[z]*Exp[+ Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}, GenerateConditions->None]
Failure Aborted
Failed [20 / 20]
Result: Float(infinity)+Float(infinity)*I
Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I}


Result: Float(infinity)+Float(infinity)*I
Test Values: {a = 1.5, z = 1/2-1/2*I*3^(1/2)}

... skip entries to safe data
 Skipped - Because timed out
8.6.E10 γ ⁡ ( a , z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ Γ ⁡ ( s ) a - s ⁢ z a - s ⁢ d s incomplete-gamma 𝑎 𝑧 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑠 𝑎 𝑠 superscript 𝑧 𝑎 𝑠 𝑠 {\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{1}{2\pi i}\int_{c-i% \infty}^{c+i\infty}\frac{\Gamma\left(s\right)}{a-s}z^{a-s}\mathrm{d}s}}
\incgamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{s}}{a-s}z^{a-s}\diff{s}		 | ph ⁡ z | < 1 2 ⁢ π , ℜ ⁡ s > 0 , ℜ ⁡ a > 0 formulae-sequence phase 𝑧 1 2 𝜋 formulae-sequence 𝑠 0 𝑎 0 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi,\Re s>0,\Re a% >0}} 
GAMMA(a)-GAMMA(a, z) = (1)/(2*Pi*I)*int((GAMMA(s))/(a - s)*(z)^(a - s), s = c - I*infinity..c + I*infinity)

Gamma[a, 0, z] == Divide[1,2*Pi*I]*Integrate[Divide[Gamma[s],a - s]*(z)^(a - s), {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]
Failure Aborted
Failed [90 / 90]
Result: .3508882474+.1990162824*I
Test Values: {a = 1.5, c = -1.5, z = 1/2*3^(1/2)+1/2*I, a = 1}


Result: .2281607298-.4280186861*I
Test Values: {a = 1.5, c = -1.5, z = 1/2-1/2*I*3^(1/2), a = 1}

... skip entries to safe data
 Skipped - Because timed out
8.6.E11 Γ ⁡ ( a , z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ Γ ⁡ ( s + a ) ⁢ z - s s ⁢ d s incomplete-Gamma 𝑎 𝑧 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑠 𝑎 superscript 𝑧 𝑠 𝑠 𝑠 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{1}{2\pi i}\int_{c-i% \infty}^{c+i\infty}\Gamma\left(s+a\right)\frac{z^{-s}}{s}\mathrm{d}s}}
\incGamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+a}\frac{z^{-s}}{s}\diff{s}		 | ph ⁡ z | < 1 2 ⁢ π , ℜ ⁡ ( s + a ) > 0 formulae-sequence phase 𝑧 1 2 𝜋 𝑠 𝑎 0 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi,\Re(s+a)>0}} 
GAMMA(a, z) = (1)/(2*Pi*I)*int(GAMMA(s + a)*((z)^(- s))/(s), s = c - I*infinity..c + I*infinity)

Gamma[a, z] == Divide[1,2*Pi*I]*Integrate[Gamma[s + a]*Divide[(z)^(- s),s], {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]
Failure Aborted
Failed [180 / 180]
Result: .1072320848e-1-.1480251451*I
Test Values: {a = -1.5, c = -1.5, z = 1/2*3^(1/2)+1/2*I}


Result: -.2224046553+.6479031822e-1*I
Test Values: {a = -1.5, c = -1.5, z = 1/2-1/2*I*3^(1/2)}

... skip entries to safe data
 Skipped - Because timed out
8.6.E12 Γ ⁡ ( a , z ) = - z a - 1 ⁢ e - z Γ ⁡ ( 1 - a ) ⁢ 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ Γ ⁡ ( s + 1 - a ) ⁢ π ⁢ z - s sin ⁡ ( π ⁢ s ) ⁢ d s incomplete-Gamma 𝑎 𝑧 superscript 𝑧 𝑎 1 superscript 𝑒 𝑧 Euler-Gamma 1 𝑎 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑠 1 𝑎 𝜋 superscript 𝑧 𝑠 𝜋 𝑠 𝑠 {\displaystyle{\displaystyle\Gamma\left(a,z\right)=-\frac{z^{a-1}e^{-z}}{% \Gamma\left(1-a\right)}\*\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\Gamma% \left(s+1-a\right)\frac{\pi z^{-s}}{\sin\left(\pi s\right)}\mathrm{d}s}}
\incGamma@{a}{z} = -\frac{z^{a-1}e^{-z}}{\EulerGamma@{1-a}}\*\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+1-a}\frac{\pi z^{-s}}{\sin@{\pi s}}\diff{s}		 | ph ⁡ z | < 3 2 ⁢ π , ℜ ⁡ ( s + 1 - a ) > 0 , ℜ ⁡ ( 1 - a ) > 0 formulae-sequence phase 𝑧 3 2 𝜋 formulae-sequence 𝑠 1 𝑎 0 1 𝑎 0 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{3}{2}\pi,\Re(s+1-a)>0,% \Re(1-a)>0}} 
GAMMA(a, z) = -((z)^(a - 1)* exp(- z))/(GAMMA(1 - a))*(1)/(2*Pi*I)*int(GAMMA(s + 1 - a)*(Pi*(z)^(- s))/(sin(Pi*s)), s = c - I*infinity..c + I*infinity)

Gamma[a, z] == -Divide[(z)^(a - 1)* Exp[- z],Gamma[1 - a]]*Divide[1,2*Pi*I]*Integrate[Gamma[s + 1 - a]*Divide[Pi*(z)^(- s),Sin[Pi*s]], {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]
Failure Aborted
Failed [168 / 168]
Result: .1072320848e-1-.1480251451*I
Test Values: {a = -1.5, c = -1.5, z = 1/2*3^(1/2)+1/2*I, a = -1}


Result: .7867555591e-1+.8824866094*I
Test Values: {a = -1.5, c = -1.5, z = -1/2+1/2*I*3^(1/2), a = -1}

... skip entries to safe data
 Skipped - Because timed out
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