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

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.agcw.01

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), -(15/4)}, z] == (1/(2371289468625 z^(1/4))) (Sqrt[2] (3 (790429822875 - 1360497392100 z + 146327504400 z^2 + 302988470400 z^3 + 123116716800 z^4 - 165032017920 z^5 + 646025969664 z^6 + 127909494784 z^7 + 989855744 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (2371289468625 - 919772884800 z - 1389613579200 z^2 - 564263884800 z^3 - 122863910400 z^4 - 327892008960 z^5 + 569762906112 z^6 + 23580377088 z^7 + 33554432 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 36 z (263476607625 + 249105156300 z + 110824005600 z^2 + 38026296000 z^3 + 20224512000 z^4 + 12707266560 z^5 + 8753512448 z^6 + 79691776 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]