Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afi8)

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.afi8.01

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), -(15/4)}, z] == -((1/(11345882625 z^(1/4))) (Sqrt[2] ((-11345882625 + 19498109400 z - 2130559200 z^2 - 4313675520 z^3 - 2004710400 z^4 + 12716605440 z^5 + 13351256064 z^6 + 260046848 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-11345882625 + 4370265900 z + 6577956000 z^2 + 2648479680 z^3 + 298045440 z^4 + 8346009600 z^5 + 1330642944 z^6 + 4194304 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-11345882625 - 10757577600 z - 4883986800 z^2 - 1829963520 z^3 - 1390878720 z^4 + 2385838080 z^5 + 61865984 z^6) BesselI[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]