Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a988)

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

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a988.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 7/4}, z] == ((-4 z (-65367225 + 30561300 z - 23284800 z^2 - 528082240 z^3 + 252902400 z^4 - 18333696 z^5 + 262144 z^6) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-196101675 + 54331200 z - 50450400 z^2 - 198881760 z^3 + 120942080 z^4 - 9084928 z^5 + 131072 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (588305025 - 50935500 z + 114483600 z^2 - 341510400 z^3 - 1886142720 z^4 + 993685504 z^5 - 73072640 z^6 + 1048576 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (1435616000 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]