Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8300)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8300.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(5/4)}, z] == (1/(2741090625 Sqrt[2])) (z^(1/4) ((2741090625 + 12404271600 z + 41020761600 z^2 - 33379180800 z^3 + 4131696640 z^4 - 132055040 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 8 Sqrt[z] (814074975 + 1607886000 z - 1937905200 z^2 + 253182720 z^3 - 8212480 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (3338822025 + 15110247600 z + 34066368000 z^2 - 32395910400 z^3 + 4099092480 z^4 - 131792896 z^5 + 1048576 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]