Generalized Hypergeometric Functions & Meijer G -Function - 16.3 Derivatives and Contiguous Functions

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
16.3.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n} = z^{n}\deriv[n]{}{z}z^{n}}
\left(z\deriv{}{z}z\right)^{n} = z^{n}\deriv[n]{}{z}z^{n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(z*diff(z, z))^(n) = (z)^(n)* diff((z)^(n), [z$(n)])

(z*D[z, z])^(n) == (z)^(n)* D[(z)^(n), {z, n}]
Failure Failure
Failed [7 / 7]
Result: -.1616869430e-8-5.000000005*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, n = 3}


Result: -5.000000005+.1616869430e-8*I
Test Values: {z = -1/2+1/2*I*3^(1/2), n = 3}

... skip entries to safe data
Failed [14 / 21]
Result: Complex[-0.5000000000000001, -0.8660254037844386]
Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.0, -5.0]
Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
16.3.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\genhyperF{0}{1}@{-}{b+1}{z}+b(b-1)\genhyperF{0}{1}@{-}{b}{z}-b(b-1)\genhyperF{0}{1}@{-}{b-1}{z} = 0}
z\genhyperF{0}{1}@{-}{b+1}{z}+b(b-1)\genhyperF{0}{1}@{-}{b}{z}-b(b-1)\genhyperF{0}{1}@{-}{b-1}{z} = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z*hypergeom([-], [b + 1], z)+ b*(b - 1)*hypergeom([-], [b], z)- b*(b - 1)*hypergeom([-], [b - 1], z) = 0

z*HypergeometricPFQ[{-}, {b + 1}, z]+ b*(b - 1)*HypergeometricPFQ[{-}, {b}, z]- b*(b - 1)*HypergeometricPFQ[{-}, {b - 1}, z] == 0
Error Failure - Error
16.3.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperF{3}{2}@@{a_{1}+2,a_{2},a_{3}}{b_{1},b_{2}}{z}a_{1}(a_{1}+1)(1-z)+\genhyperF{3}{2}@@{a_{1}+1,a_{2},a_{3}}{b_{1},b_{2}}{z}a_{1}\left(b_{1}+b_{2}-3a_{1}-2+z(2a_{1}-a_{2}-a_{3}+1)\right)+\genhyperF{3}{2}@@{a_{1},a_{2},a_{3}}{b_{1},b_{2}}{z}\left((2a_{1}-b_{1})(2a_{1}-b_{2})+a_{1}-a_{1}^{2}-z(a_{1}-a_{2})(a_{1}-a_{3})\right)-\genhyperF{3}{2}@@{a_{1}-1,a_{2},a_{3}}{b_{1},b_{2}}{z}(a_{1}-b_{1})(a_{1}-b_{2}) = 0}
\genhyperF{3}{2}@@{a_{1}+2,a_{2},a_{3}}{b_{1},b_{2}}{z}a_{1}(a_{1}+1)(1-z)+\genhyperF{3}{2}@@{a_{1}+1,a_{2},a_{3}}{b_{1},b_{2}}{z}a_{1}\left(b_{1}+b_{2}-3a_{1}-2+z(2a_{1}-a_{2}-a_{3}+1)\right)+\genhyperF{3}{2}@@{a_{1},a_{2},a_{3}}{b_{1},b_{2}}{z}\left((2a_{1}-b_{1})(2a_{1}-b_{2})+a_{1}-a_{1}^{2}-z(a_{1}-a_{2})(a_{1}-a_{3})\right)-\genhyperF{3}{2}@@{a_{1}-1,a_{2},a_{3}}{b_{1},b_{2}}{z}(a_{1}-b_{1})(a_{1}-b_{2}) = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
hypergeom([a[1]+ 2 , a[2], a[3]], [b[1], b[2]], z)*a[1]*(a[1]+ 1)*(1 - z)+ hypergeom([a[1]+ 1 , a[2], a[3]], [b[1], b[2]], z)*a[1]*(b[1]+ b[2]- 3*a[1]- 2 + z*(2*a[1]- a[2]- a[3]+ 1))+ hypergeom([a[1], a[2], a[3]], [b[1], b[2]], z)*((2*a[1]- b[1])*(2*a[1]- b[2])+ a[1]- (a[1])^(2)- z*(a[1]- a[2])*(a[1]- a[3]))- hypergeom([a[1]- 1 , a[2], a[3]], [b[1], b[2]], z)*(a[1]- b[1])*(a[1]- b[2]) = 0

HypergeometricPFQ[{Subscript[a, 1]+ 2 , Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z]*Subscript[a, 1]*(Subscript[a, 1]+ 1)*(1 - z)+ HypergeometricPFQ[{Subscript[a, 1]+ 1 , Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z]*Subscript[a, 1]*(Subscript[b, 1]+ Subscript[b, 2]- 3*Subscript[a, 1]- 2 + z*(2*Subscript[a, 1]- Subscript[a, 2]- Subscript[a, 3]+ 1))+ HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z]*((2*Subscript[a, 1]- Subscript[b, 1])*(2*Subscript[a, 1]- Subscript[b, 2])+ Subscript[a, 1]- (Subscript[a, 1])^(2)- z*(Subscript[a, 1]- Subscript[a, 2])*(Subscript[a, 1]- Subscript[a, 3]))- HypergeometricPFQ[{Subscript[a, 1]- 1 , Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z]*(Subscript[a, 1]- Subscript[b, 1])*(Subscript[a, 1]- Subscript[b, 2]) == 0
Failure Failure Skipped - Because timed out
Failed [300 / 300]
Result: Plus[Complex[1.7372028395654344, 0.5250871122698257], Times[Complex[-0.5000000000000001, -0.8660254037844386], a]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Plus[Complex[4.427028162877593, -11.419461015230842], Times[Complex[-0.5000000000000001, -0.8660254037844386], a]]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
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