Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9op)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9op.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 23/4}, -z] == (1/(889058230272 z^(19/4))) (Sqrt[Pi] (6374765194875 - 15866082262800 z + 9890544787200 z^2 - 3425296896000 z^3 + 1217883340800 z^4 + 615351582720 z^5 + 28538044416 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-996426876375 + 636607188000 z - 216586379520 z^2 + 69595545600 z^3 + 38131924992 z^4 + 1780482048 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (-132067978875 + 548847381600 z - 193495599360 z^2 + 46092533760 z^3 + 36849254400 z^4 + 1767899136 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))

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]