Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7998)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.7998.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), -(19/4)}, z] == (1/124428150) ((62214075 + 62214075 E^(4 Sqrt[z]) + 124428150 Sqrt[z] - 124428150 E^(4 Sqrt[z]) Sqrt[z] + 107692200 z + 107692200 E^(4 Sqrt[z]) z + 49480200 z^(3/2) - 49480200 E^(4 Sqrt[z]) z^(3/2) + 11032560 z^2 + 11032560 E^(4 Sqrt[z]) z^2 + 332640 z^(5/2) - 332640 E^(4 Sqrt[z]) z^(5/2) - 120960 z^3 - 120960 E^(4 Sqrt[z]) z^3 + 53760 z^(7/2) - 53760 E^(4 Sqrt[z]) z^(7/2) - 30720 z^4 - 30720 E^(4 Sqrt[z]) z^4 + 24576 z^(9/2) - 24576 E^(4 Sqrt[z]) z^(9/2) - 32768 z^5 - 32768 E^(4 Sqrt[z]) z^5 + 131072 z^(11/2) - 131072 E^(4 Sqrt[z]) z^(11/2) + 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) Erf[Sqrt[2] z^(1/4)] + 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Rule 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]