Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af3i)

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`=-7/2

http://functions.wolfram.com/07.22.03.af3i.01

Input Form

HypergeometricPFQ[{17/4}, {-(7/2), -(17/4)}, z] == -((1/(610871625 Sqrt[2])) (z^(1/4) (3 (-203623875 - 465426000 z - 379501200 z^2 - 161241600 z^3 - 95047680 z^4 + 357826560 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 + 4 Sqrt[z] (610871625 + 907580700 z + 455878800 z^2 + 178214400 z^3 + 167731200 z^4 + 189661184 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (-610871625 - 418883400 z - 164211840 z^2 - 71285760 z^3 + 223936512 z^4 + 12320768 z^5) 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]