Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adq1)

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

For fixed z and a₁=11/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.adq1.01

Input Form

HypergeometricPFQ[{11/4}, {-(9/2), -(23/4)}, -z] == (1/(30049398225 z^(1/4))) (Sqrt[2] (7 (4292771175 + 8129305800 z + 2000829600 z^2 - 1572721920 z^3 + 350622720 z^4 - 53379072 z^5 - 16515072 z^6 + 16777216 z^7) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (30049398225 + 16839276300 z - 16078154400 z^2 + 4301760960 z^3 - 692858880 z^4 + 77070336 z^5 - 154140672 z^6 + 4194304 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (-30049398225 + 23226588000 z - 7259036400 z^2 + 1328221440 z^3 - 206438400 z^4 + 67436544 z^5 + 26214400 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^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]