Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agf8)

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`=-9/2

http://functions.wolfram.com/07.22.03.agf8.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), 21/4}, z] == -((221 (2 Sqrt[z] (-5189960350575 + 4339541939040 z + 1643191038720 z^2 + 247008706560 z^3 + 27362918400 z^4 + 2812280832 z^5 - 83886080 z^6) BesselI[1/4, Sqrt[z]]^2 + (25949801752875 - 40150902052800 z - 20545121076480 z^2 - 3820545146880 z^3 - 439020748800 z^4 - 48129638400 z^5 - 1090519040 z^6 + 134217728 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (25949801752875 + 15208675020000 z + 3464307221760 z^2 + 450745712640 z^3 + 47721676800 z^4 + 3114270720 z^5 - 134217728 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(362423255040 Sqrt[2] z^(15/4)))

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]