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

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-9/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), 23/4}, z] == -((209 (-2 Sqrt[z] (213530411469375 + 247112671806000 z + 56863314144000 z^2 + 6149109657600 z^3 + 408717557760 z^4 + 21092106240 z^5 + 721420288 z^6) BesselI[-(1/4), Sqrt[z]]^2 + (640591234408125 + 1717477039278000 z + 610611988896000 z^2 + 88156247961600 z^3 + 7136472268800 z^4 + 402228510720 z^5 + 18270388224 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 30 Sqrt[z] (42706082293875 + 23392160391600 z + 4687056541440 z^2 + 479237713920 z^3 + 31068979200 z^4 + 1571815424 z^5 + 50331648 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (250274119680 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]