Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ta)

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`=7/2

http://functions.wolfram.com/07.22.03.a7ta.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, -(3/4)}, z] == (1/(245301210 Sqrt[2] z^(5/4))) ((32 z (14022315 - 4318920 z - 79534080 z^2 + 34468992 z^3 - 2371584 z^4 + 32768 z^5) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-17453475 - 144797760 z - 210643200 z^2 + 129768960 z^3 - 9371648 z^4 + 131072 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-261802125 + 257774400 z + 1164741120 z^2 + 1789378560 z^3 - 1047121920 z^4 + 75104256 z^5 - 1048576 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]