Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8gm)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a8gm.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(7/2), 21/4}, z] == -((17 (2 Sqrt[z] (-86746480145325 + 102938199764400 z - 4762114156800 z^2 + 480613478400 z^3 + 910820966400 z^4 + 129110114304 z^5 + 8002732032 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 - 3 (-144577466908875 + 274374309409200 z + 24717640147200 z^2 + 1539952128000 z^3 + 1037367705600 z^4 + 136508866560 z^5 + 8237613056 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (-433732400726625 - 102172859989200 z - 2818394092800 z^2 + 1321422336000 z^3 + 1016340480000 z^4 + 135376404480 z^5 + 8204058624 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(24415882444800 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]