Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0580)

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

For fixed z and a₁=-11/2, b₁=2

http://functions.wolfram.com/07.22.03.0580.01

Input Form

HypergeometricPFQ[{-(11/2)}, {2, 5}, -z] == (1/(29492271183375 z^3)) (32 (2 z (-4214184975 - 5618913300 z + 589985896500 z^2 + 733665794400 z^3 + 168068432160 z^4 + 11632011264 z^5 + 293693952 z^6 + 2785280 z^7 + 8192 z^8) BesselJ[0, Sqrt[z]]^2 - Sqrt[z] (-33713479800 - 40737121425 z + 471988717200 z^2 + 1249201245600 z^3 + 319625737920 z^4 + 22832716032 z^5 + 583237632 z^6 + 5558272 z^7 + 16384 z^8) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + 2 (-16856739900 - 18261468225 z - 44951306400 z^2 + 320490116100 z^3 + 657523972080 z^4 + 162464318496 z^5 + 11487227904 z^6 + 292307456 z^7 + 2781184 z^8 + 8192 z^9) 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]