Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9187)

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`=-9/2

http://functions.wolfram.com/07.22.03.9187.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 17/4}, -z] == (13 (Sqrt[Pi] (3754736699781375 + 1722603217104000 z + 714561334502400 z^2 + 994172291481600 z^3 - 348832382976000 z^4 + 42524328591360 z^5 - 2811525857280 z^6 + 122406567936 z^7 - 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-3754736699781375 + 2282449262662800 z + 105725911737600 z^2 - 25335886786560 z^3 + 2859605360640 z^4 - 183883530240 z^5 + 7902068736 z^6 - 268435456 z^7) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-1251578899927125 - 2050718115600 z - 68163936825600 z^2 + 22400146944000 z^3 - 2694537216000 z^4 + 177264918528 z^5 - 7700742144 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (14546538835476480 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]