Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8954)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8954.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(23/4)}, z] == ((-16 z (-679242137805 + 42977021018400 z + 9085690010880 z^2 + 776056651776 z^3 + 36040015872 z^4 + 1012924416 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (208703679809625 + 104812287672960 z + 19651595604480 z^2 + 1618394480640 z^3 + 73902194688 z^4 + 2055208960 z^5 + 33554432 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-3130555197144375 + 708327640566000 z + 811117215659520 z^2 + 155306682961920 z^3 + 12866149416960 z^4 + 589059588096 z^5 + 16408117248 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(255878352873990 Sqrt[2] z^(5/4))

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]