Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af7j)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.af7j.01

Input Form

HypergeometricPFQ[{17/4}, {-(1/2), -(17/4)}, -z] == -((1/(5817825 Sqrt[2])) (z^(1/4) ((-5817825 + 23271300 z - 11456640 z^2 - 46868480 z^3 - 16285696 z^4 + 262144 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-5817825 + 18617040 z + 30059520 z^2 + 2609152 z^3 + 2031616 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (5817825 + 6314400 z - 10338816 z^2 - 3579904 z^3 + 65536 z^4) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]