Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8343)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8343.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(11/4)}, -z] == (1/(93270177000 z^(3/2))) (-2 Sqrt[z] (15058768725 - 5297292000 z + 1228711680 z^2 - 464240640 z^3 + 609812480 z^4 + 43220992 z^5 + 524288 z^6) Cos[2 Sqrt[z]] - 32768 Sqrt[Pi] z^(21/4) (316825 + 21344 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (15058768725 + 21259438200 z - 4976294400 z^2 + 1371310080 z^3 - 840499200 z^4 + 5127012352 z^5 + 348913664 z^6 + 4194304 z^7) 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]