Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8782)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.8782.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), -(3/4)}, z] == (1/(1091475 z^(1/4))) (Sqrt[2] ((1091475 - 17463600 z + 291060000 z^2 - 458932320 z^3 + 137829888 z^4 - 9117696 z^5 + 131072 z^6) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-363825 + 5336100 z - 43866900 z^2 + 16255680 z^3 - 1125376 z^4 + 16384 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (1091475 - 14553000 z + 91035000 z^2 - 32780160 z^3 + 2254848 z^4 - 32768 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]