Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9045)

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`=9/2

http://functions.wolfram.com/07.22.03.9045.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 19/4}, -z] == (Sqrt[Pi] (-2140002301154342625 + 9338191859582586000 z - 12196822020679296000 z^2 + 13798424912283648000 z^3 + 22077479859653836800 z^4 + 3718312397415383040 z^5 + 191603859448135680 z^6 + 3743176741355520 z^7 + 28411208663040 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (478671476827123125 - 693459792393076800 z + 674816116707532800 z^2 + 1340638754004910080 z^3 + 230240748965068800 z^4 + 11932093277798400 z^5 + 233617364090880 z^6 + 1774895235072 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-244008853269465375 - 177607439579606400 z + 133327883025792000 z^2 + 1199337049593446400 z^3 + 221975009846231040 z^4 + 11762327586078720 z^5 + 232299681546240 z^6 + 1771674009600 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(23753004300506234880 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]