Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9kn)

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`=5/2

http://functions.wolfram.com/07.22.03.a9kn.01

Input Form

HypergeometricPFQ[{-(9/4)}, {5/2, 21/4}, -z] == (17 (2 Sqrt[z] (-383107725 - 778377600 z - 997920000 z^2 + 11127029760 z^3 + 9296216064 z^4 + 931135488 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]]^2 - 3 (-638512875 - 1751349600 z - 1902700800 z^2 + 4257792000 z^3 + 8506245120 z^4 + 916455424 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-1915538625 - 1167566400 z - 2594592000 z^2 + 5020876800 z^3 + 8614379520 z^4 + 918552576 z^5 + 16777216 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(139882659840 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]