Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af0u)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.af0u.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), -(17/4)}, z] == -((1/(60476290875 Sqrt[2])) (z^(1/4) ((-60476290875 - 131948271000 z - 96536512800 z^2 - 30207340800 z^3 - 7057290240 z^4 - 3220439040 z^5 + 5986058240 z^6 + 226492416 z^7) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (60476290875 + 83567238300 z + 33983258400 z^2 + 8433996480 z^3 + 2063093760 z^4 + 573112320 z^5 + 963641344 z^6 + 4194304 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (-60476290875 - 35186205600 z - 10134830160 z^2 - 2298965760 z^3 - 704471040 z^4 + 1269104640 z^5 + 55574528 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]