Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8480)

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/07.22.03.8480.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(17/4)}, z] == -(((4 z (783627455676594375 - 38381752931098500 z + 13841228706782400 z^2 - 11300588895974400 z^3 - 4007625276211200 z^4 - 528535305584640 z^5 - 42534793379840 z^6 - 2742672162816 z^7 - 254476812288 z^8 + 8589934592 z^9) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-2350882367029783125 - 332641858736187000 z + 3670412569084800 z^2 + 7765164978278400 z^3 + 2225781286502400 z^4 + 280672964444160 z^5 + 22288237854720 z^6 + 1443645882368 z^7 + 124554051584 z^8 - 4294967296 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (7052647101089349375 + 2341286928797008500 z + 109284819098439600 z^2 - 29950261648876800 z^3 + 50580513510912000 z^4 + 16653344838451200 z^5 + 2162194702663680 z^6 + 173216215597056 z^7 + 11211743690752 z^8 + 1009317314560 z^9 - 34359738368 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (20420884721952000 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]