Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9bd)

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`=-9/2

http://functions.wolfram.com/07.22.03.a9bd.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(9/2), 23/4}, -z] == (209 (Sqrt[Pi] (-640591234408125 - 129272465322000 z - 17093879712000 z^2 - 2245501440000 z^3 - 479040307200 z^4 + 218989854720 z^5 - 13740539904 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-213530411469375 + 54523080612000 z - 1775282745600 z^2 - 32901120000 z^3 + 13854769152 z^4 - 861929472 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (640591234408125 - 554024851380000 z + 52739076499200 z^2 - 384723763200 z^3 + 14553907200 z^4 - 874512384 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(92358976733184 z^(19/4))

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]