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

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`=11/2

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

Input Form

HypergeometricPFQ[{21/4}, {11/2, -(21/4)}, z] == (1/(562648320 Sqrt[2] z^(15/4))) ((4 z (20183179141125 + 6210208966500 z + 818503237440 z^2 + 64693463040 z^3 + 4347494400 z^4 + 276037632 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (60549537423375 + 30163872123000 z + 5405070928320 z^2 + 522674933760 z^3 + 35791994880 z^4 + 2480406528 z^5 + 96468992 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (181648612270125 + 125091352039500 z + 31654322274960 z^2 + 3898178161920 z^3 + 301087825920 z^4 + 20213268480 z^5 + 1204813824 z^6 + 16777216 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]