Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9138)

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`=-11/2

http://functions.wolfram.com/07.22.03.9138.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 17/4}, z] == (13 (-4 z^(1/4) (-43805261497449375 - 58407015329932500 Sqrt[z] - 28925379020538000 z - 2966705540568000 z^(3/2) + 689041286841600 z^2 - 2040278096102400 z^(5/2) + 153646270525440 z^3 - 563556069457920 z^(7/2) + 13967642787840 z^4 - 53670653460480 z^(9/2) + 662034186240 z^5 - 2591060656128 z^(11/2) + 18102616064 z^6 - 71605157888 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (-43805261497449375 + 58407015329932500 Sqrt[z] - 28925379020538000 z + 2966705540568000 z^(3/2) + 689041286841600 z^2 + 2040278096102400 z^(5/2) + 153646270525440 z^3 + 563556069457920 z^(7/2) + 13967642787840 z^4 + 53670653460480 z^(9/2) + 662034186240 z^5 + 2591060656128 z^(11/2) + 18102616064 z^6 + 71605157888 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-43805261497449375 + 17800233243408000 z - 6431052010521600 z^2 + 7621987568025600 z^3 + 2209271758848000 z^4 + 212621642956800 z^5 + 10308928143360 z^6 + 285615325184 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-43805261497449375 + 17800233243408000 z - 6431052010521600 z^2 + 7621987568025600 z^3 + 2209271758848000 z^4 + 212621642956800 z^5 + 10308928143360 z^6 + 285615325184 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(426698472507310080 z^(13/4))

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]