Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9706)

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`=-11/2

http://functions.wolfram.com/07.22.03.9706.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), 9/4}, z] == ((-2 Sqrt[z] (-54552126321 + 49847401296 z + 13741668864 z^2 + 1274093568 z^3 + 54460416 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 + 3 (27105783705 + 57127560336 z + 14943785472 z^2 + 1323294720 z^3 + 55377920 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (81317351115 + 61597310544 z + 14754009600 z^2 + 1315971072 z^3 + 55246848 z^4 + 1048576 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(70815596544 Sqrt[2] z^(3/4))

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]