Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9710)

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/07.22.03.9710.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), 13/4}, z] == ((-2 Sqrt[z] (-2520837884565 + 658891449216 z + 2197887664896 z^2 + 414223958016 z^3 + 29600317440 z^4 + 1031798784 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (-4201396474275 + 9541235864160 z + 2612006901504 z^2 + 441757679616 z^3 + 30527913984 z^4 + 1046478848 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-12604189422825 + 1734770157120 z + 2541208640256 z^2 + 437490450432 z^3 + 30390681600 z^4 + 1044381696 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (3273254240256 Sqrt[2] z^(7/4))

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]