Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adu0)

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`=-3/2

http://functions.wolfram.com/07.22.03.adu0.01

Input Form

HypergeometricPFQ[{11/4}, {-(3/2), -(23/4)}, z] == (1/(95394915 z^(1/4))) (Sqrt[2] ((95394915 - 160374060 z + 26777520 z^2 - 17740800 z^3 + 77414400 z^4 - 4718592 z^5 + 1048576 z^6) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (95394915 - 33180840 z - 41690880 z^2 - 59028480 z^3 - 14057472 z^4 + 3407872 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (95394915 + 94012380 z + 59431680 z^2 + 27033600 z^3 - 3538944 z^4 + 262144 z^5) 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]