Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vu)

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.a7vu.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(7/4)}, z] == ((-4 z (654243510375 - 116309957400 z - 14538908160 z^2 + 58902681600 z^3 + 22687580160 z^4 + 13002866688 z^5 - 1893728256 z^6 + 33554432 z^7) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (1090405850625 - 96924964500 z + 34083504000 z^2 + 43978798080 z^3 + 15744368640 z^4 + 5697699840 z^5 - 932184064 z^6 + 16777216 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-16356087759375 - 332314164000 z^2 + 234173721600 z^3 + 335274024960 z^4 + 122706984960 z^5 + 46462402560 z^6 - 7474249728 z^7 + 134217728 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(94631755680 Sqrt[2] z^(13/4))

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]