Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a820)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.a820.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(5/2), 23/4}, z] == -((19 (2 Sqrt[z] (605964681196875 + 503080037460000 z - 24083002944000 z^2 + 5175346176000 z^3 - 4663561420800 z^4 - 1712377036800 z^5 - 260214620160 z^6 - 34896609280 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 + (-1817894043590625 - 4279364369280000 z - 270470648448000 z^2 - 5645832192000 z^3 + 5906409062400 z^4 + 1883661926400 z^5 + 274810798080 z^6 + 32212254720 z^7 - 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (1817894043590625 + 401190409620000 z + 5557616064000 z^2 - 3626361446400 z^3 + 5177475072000 z^4 + 1783155916800 z^5 + 267261050880 z^6 + 33822867456 z^7 - 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(160175436595200 Sqrt[2] z^(17/4)))

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]