Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8479)

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`=11/2

http://functions.wolfram.com/07.22.03.8479.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(19/4)}, -z] == (-2 Sqrt[z] (29393528790816815625 - 10289626552255050000 z - 198089067316140000 z^2 + 4047797033280000 z^3 - 112634352230400 z^4 + 4516665753600 z^5 - 283398635520 z^6 + 31708938240 z^7 - 8053063680 z^8 + 8589934592 z^9) Cos[2 Sqrt[z]] - 137438953472 Sqrt[Pi] z^(41/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (29393528790816815625 - 49480998273344137500 z + 3070380543400170000 z^2 - 54645259949280000 z^3 + 1295295050649600 z^4 - 42908324659200 z^5 + 2125489766400 z^6 - 174399160320 z^7 + 28185722880 z^8 - 12884901888 z^9 + 68719476736 z^10) Sin[2 Sqrt[z]])/ (270368817630912000 z^(9/2))

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]