Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8224)

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`=-1/2

http://functions.wolfram.com/07.22.03.8224.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 15/4}, z] == ((-2 Sqrt[z] (61665657928875 - 21684626964000 z - 662954742028800 z^2 - 2308342485196800 z^3 + 4600781321011200 z^4 - 952066312765440 z^5 + 51785393766400 z^6 - 892816326656 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 + (184996973786625 + 216846269640000 z + 46260537523200 z^2 - 554222750515200 z^3 + 4083007183257600 z^4 - 921150129438720 z^5 + 51234597765120 z^6 - 890131972096 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (-184996973786625 + 177813941104800 z - 485735643993600 z^2 - 1449948692275200 z^3 + 4381429963161600 z^4 - 939460814438400 z^5 + 51563867406336 z^6 - 891742584832 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1555610075136000 Sqrt[2] z^(9/4))

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]