Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8349)

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/07.22.03.8349.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(5/4)}, -z] == ((8 z (15288995925 - 40699184400 z + 89391859200 z^2 + 56745767680 z^3 + 5701201920 z^4 + 153157632 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (12242347425 - 47267967600 z + 61883942400 z^2 + 53427575040 z^3 + 5607239680 z^4 + 152502272 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (36727042275 + 169166982600 z - 390929212800 z^2 + 617360486400 z^3 + 443026913280 z^4 + 45306576896 z^5 + 1223163904 z^6 + 8388608 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(105988837500 Sqrt[2] z^(3/4))

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]