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

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

For fixed z and a₁=11/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(7/2), -(23/4)}, z] == (1/(3338822025 z^(1/4))) (Sqrt[2] ((3338822025 - 6221407500 z + 1385445600 z^2 + 1240303680 z^3 + 318044160 z^4 - 8945664 z^5 + 128450560 z^6 + 4194304 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (3338822025 - 1769644800 z - 1822035600 z^2 - 534078720 z^3 - 91176960 z^4 - 67436544 z^5 + 24117248 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (3338822025 + 2682117900 z + 906166800 z^2 + 198535680 z^3 + 57630720 z^4 + 14811136 z^5 + 1048576 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]