Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8484)

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`=11/2

http://functions.wolfram.com/07.22.03.8484.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(13/4)}, z] == ((4 z (-67168067629422375 + 6190605311467500 z - 1947643637385600 z^2 + 1834979591808000 z^3 + 848935246233600 z^4 + 156917850439680 z^5 + 20925005168640 z^6 + 4229267718144 z^7 - 380373041152 z^8 + 4294967296 z^9) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-201504202888267125 - 19809936996696000 z - 311584867624800 z^2 + 1353556813593600 z^3 + 493358813798400 z^4 + 86672631398400 z^5 + 11489677148160 z^6 + 1999374385152 z^7 - 188844343296 z^8 + 2147483648 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (604512608664801375 + 174575069783383500 z + 6273146715620400 z^2 - 4014933212505600 z^3 + 8556315528499200 z^4 + 3593793668382720 z^5 + 652724105379840 z^6 + 87366580568064 z^7 + 16543408717824 z^8 - 1517197197312 z^9 + 17179869184 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(3603685539168000 Sqrt[2] z^(15/4))

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]