Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af2y)

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`=-9/2

http://functions.wolfram.com/07.22.03.af2y.01

Input Form

HypergeometricPFQ[{17/4}, {-(9/2), 11/4}, z] == -((1/(13478400 Sqrt[2] z^(5/4))) ((10 Sqrt[z] (-3132675 - 6598800 z - 2695680 z^2 + 638976 z^3 + 16384 z^4) BesselI[-(1/4), Sqrt[z]]^2 + (46990125 + 150368400 z + 130291200 z^2 - 4792320 z^3 - 5406720 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 6 Sqrt[z] (-15663375 - 16707600 z - 3893760 z^2 + 1290240 z^3 + 16384 z^4) BesselI[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]