Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab0v)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ab0v.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(11/2), -(19/4)}, -z] == (1/(684354825 z^(1/4))) (Sqrt[2] ((684354825 + 1375258500 z + 469188720 z^2 - 213171840 z^3 + 27465984 z^4 - 1720320 z^5 + 65536 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (228118275 + 154261800 z - 107220960 z^2 + 18681600 z^3 - 1498112 z^4 + 65536 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (684354825 - 449687700 z + 104116320 z^2 - 10704960 z^3 + 589824 z^4 - 16384 z^5) 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]