Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0918)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=2

http://functions.wolfram.com/07.22.03.0918.01

Input Form

HypergeometricPFQ[{-(9/2)}, {2, 4}, -z] == (1/(7023641625 z^2)) (4 (z (-9823275 + 2200413600 z + 2855412000 z^2 + 638657280 z^3 + 39202560 z^4 + 761856 z^5 + 4096 z^6) BesselJ[0, Sqrt[z]]^2 - 4 Sqrt[z] (-9823275 + 206288775 z + 608844600 z^2 + 152624880 z^3 + 9659520 z^4 + 189696 z^5 + 1024 z^6) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + (-39293100 - 127702575 z + 1150556400 z^2 + 2563247520 z^3 + 619614720 z^4 + 38824704 z^5 + 759808 z^6 + 4096 z^7) BesselJ[1, Sqrt[z]]^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]