Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9bb)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a9bb.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(9/2), 21/4}, -z] == (17 (2 Sqrt[z] (-5189960350575 - 5799574740960 z + 177925144320 z^2 - 14998781952 z^3 + 11121131520 z^4 - 786432000 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]]^2 - 3 (-8649933917625 - 15817022020800 z + 2675854621440 z^2 - 49617469440 z^3 + 11834032128 z^4 - 801112064 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-25949801752875 + 7908511010400 z - 408181213440 z^2 - 24164352000 z^3 + 11727470592 z^4 - 799014912 z^5 + 16777216 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(325545099264 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]