Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bg)

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`=11/2

http://functions.wolfram.com/07.22.03.a8bg.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(21/4)}, z] == ((4 z (-23311571907999375 - 1024684479472500 z - 102202296134400 z^2 + 62321514393600 z^3 + 11767018291200 z^4 + 721095229440 z^5 + 20719861760 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-69934715723998125 - 16394951671560000 z - 200146163263200 z^2 + 35585028864000 z^3 + 6127814246400 z^4 + 367248015360 z^5 + 10443816960 z^6 + 134217728 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (209804147171994375 + 89147549714107500 z + 7892998161879600 z^2 - 320893230873600 z^3 + 262352369664000 z^4 + 47823519744000 z^5 + 2905520209920 z^6 + 83147882496 z^7 + 1073741824 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(94229527392000 Sqrt[2] z^(15/4))

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]