Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8304)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8304.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(1/4)}, z] == -((1/(4933963125 Sqrt[2])) (z^(1/4) ((-4933963125 - 83614129200 z + 171726571800 z^2 - 49704710400 z^3 + 3713310720 z^4 - 84869120 z^5 + 524288 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-3503039400 + 18249107625 z - 5940043200 z^2 + 457643520 z^3 - 10567680 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (4292771175 + 54672181200 z - 160604451000 z^2 + 48808569600 z^3 - 3692298240 z^4 + 84738048 z^5 - 524288 z^6) 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]