Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9139)

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/07.22.03.9139.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 17/4}, -z] == (13 (Sqrt[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) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-43805261497449375 + 28925379020538000 z + 689041286841600 z^2 - 153646270525440 z^3 + 13967642787840 z^4 - 662034186240 z^5 + 18102616064 z^6 - 268435456 z^7) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-14601753832483125 + 741676385142000 z - 510069524025600 z^2 + 140889017364480 z^3 - 13417663365120 z^4 + 647765164032 z^5 - 17901289472 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (106674618126827520 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]