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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(7/2), -(23/4)}, z] == (1/(550905634125 z^(1/4))) (Sqrt[2] ((550905634125 - 971783851500 z + 138695911200 z^2 + 211207106880 z^3 + 78673351680 z^4 - 45302906880 z^5 + 139882659840 z^6 + 23391633408 z^7 + 67108864 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (550905634125 - 237243006000 z - 317540638800 z^2 - 118010027520 z^3 - 21033492480 z^4 - 57224724480 z^5 + 43426775040 z^6 + 1040187392 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (550905634125 + 497297839500 z + 205610605200 z^2 + 63757774080 z^3 + 33977180160 z^4 + 6120407040 z^5 + 5080350720 z^6 + 16777216 z^7) 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]