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

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.agco.01

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), -(23/4)}, z] == (Sqrt[2] ((1036253497789125 - 1884097268707500 z + 343765115694000 z^2 + 400933380355200 z^3 + 114657056236800 z^4 + 22272041594880 z^5 + 8931144499200 z^6 + 77455027077120 z^7 + 9145210109952 z^8 + 53418655744 z^9) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (1036253497789125 - 502425938322000 z - 589311626904000 z^2 - 193415098060800 z^3 - 40294812096000 z^4 - 7033276293120 z^5 + 3986655805440 z^6 + 17065133998080 z^7 + 485901729792 z^8 + 536870912 z^9) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (1036253497789125 + 879245392063500 z + 319840071012000 z^2 + 73538032075200 z^3 + 14861982643200 z^4 + 4316719841280 z^5 + 7973311610880 z^6 + 1931539906560 z^7 + 12952010752 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(1036253497789125 z^(1/4))

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]