Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8440)

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/07.22.03.8440.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(9/4)}, z] == -(((4 z (-57320419550625 + 20507181156000 z - 31745659968000 z^2 - 26299610726400 z^3 - 9646497792000 z^4 - 4910638694400 z^5 + 1054579097600 z^6 - 35735470080 z^7 + 268435456 z^8) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (171961258651875 - 28767018010500 z + 24769971072000 z^2 + 16482984883200 z^3 + 5659051622400 z^4 + 2154214195200 z^5 - 516347658240 z^6 + 17783848960 z^7 - 134217728 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (-515883775955625 - 11962522341000 z - 52767015840000 z^2 + 163342259942400 z^3 + 117063489945600 z^4 + 42091964006400 z^5 + 18641835786240 z^6 - 4183000350720 z^7 + 142673444864 z^8 - 1073741824 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(76062781080000 Sqrt[2] z^(11/4)))

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]