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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, -(23/4)}, z] == -((1/(739431968 Sqrt[2] z^(13/4))) (3 (4 z (505324494675 + 31301556000 z + 754130432 z^2 + 122290176 z^3 + 3145728 z^4) BesselI[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (2526622473375 + 381096444300 z + 10620403200 z^2 + 212175872 z^3 + 4718592 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (12633112366875 + 3028425543000 z + 184086988800 z^2 - 466969600 z^3 - 498597888 z^4 - 12582912 z^5) 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]