Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7u6)

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`=9/2

http://functions.wolfram.com/07.22.03.a7u6.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(19/4)}, z] == ((-4 z (-29814811401375 + 1399014529920 z + 4115059683840 z^2 + 655722676224 z^3 + 44360663040 z^4 + 1635778560 z^5 + 33554432 z^6) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-49691352335625 + 3212370252000 z + 2383724125440 z^2 + 348586721280 z^3 + 22920757248 z^4 + 832569344 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (745370285034375 + 18069582667500 z + 21268106496000 z^2 + 18625039534080 z^3 + 2762818191360 z^4 + 182482108416 z^5 + 6643777536 z^6 + 134217728 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(6357226158360 Sqrt[2] z^(9/4))

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]