Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8565)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.8565.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 19/4}, -z] == ((-Sqrt[Pi]) (8918951756664324375 + 3155599638721530000 z + 874278687784320000 z^2 + 375169398589440000 z^3 - 360162622645862400 z^4 + 54881923450798080 z^5 - 3826190741667840 z^6 + 155246961623040 z^7 - 4058744094720 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (2972983918888108125 - 307211816679768000 z + 30221979330816000 z^2 - 23286547289456640 z^3 + 3479714729164800 z^4 - 241071166586880 z^5 + 9752260116480 z^6 - 254476812288 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-8918951756664324375 + 6357948901720416000 z + 75554948327040000 z^2 - 27118471790592000 z^3 + 3700756003553280 z^4 - 249311526912000 z^5 + 9956606607360 z^6 - 257698037760 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(598486169231032320 z^(15/4))

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]