Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9334)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.9334.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(3/2), 21/4}, z] == -((221 (-4 z^(1/4) (-2624278338556875 - 3499037784742500 Sqrt[z] - 1535363736984000 z + 85595190912000 z^(3/2) + 164182588416000 z^2 - 118859457024000 z^(5/2) - 6261508915200 z^3 + 128919129292800 z^(7/2) - 18890476093440 z^4 + 98127768453120 z^(9/2) - 6547329515520 z^5 + 44528408985600 z^(11/2) + 7374593064960 z^6 - 30681367314432 z^(13/2) - 409095634944 z^7 + 1649267441664 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-2624278338556875 + 3499037784742500 Sqrt[z] - 1535363736984000 z - 85595190912000 z^(3/2) + 164182588416000 z^2 + 118859457024000 z^(5/2) - 6261508915200 z^3 - 128919129292800 z^(7/2) - 18890476093440 z^4 - 98127768453120 z^(9/2) - 6547329515520 z^5 - 44528408985600 z^(11/2) + 7374593064960 z^6 + 30681367314432 z^(13/2) - 409095634944 z^7 - 1649267441664 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-2624278338556875 + 1263866490810000 z - 473026055040000 z^2 + 235461858508800 z^3 - 513734964019200 z^4 - 391417115443200 z^5 - 198815042764800 z^6 + 123936650035200 z^7 - 6609954668544 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-2624278338556875 + 1263866490810000 z - 473026055040000 z^2 + 235461858508800 z^3 - 513734964019200 z^4 - 391417115443200 z^5 - 198815042764800 z^6 + 123936650035200 z^7 - 6609954668544 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(598486169231032320 z^(17/4)))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]