Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8850)

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/07.22.03.8850.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 17/4}, z] == ((2 Sqrt[z] (-28584816685425 + 64676756944800 z + 1938790989273600 z^2 - 8261721241804800 z^3 + 6378649288704000 z^4 - 1089042294767616 z^5 + 55006552129536 z^6 - 913217421312 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 - 3 (-47641361142375 + 141672896164800 z - 183030822374400 z^2 - 3987448606310400 z^3 + 5501282992128000 z^4 - 1042231842570240 z^5 + 54213828673536 z^6 - 909459324928 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (142924083427125 - 120113977183200 z + 246387645504000 z^2 + 4404291978240000 z^3 - 5613365211955200 z^4 + 1048673381253120 z^5 - 54325866921984 z^6 + 909996195840 z^7 - 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(2033194460774400 Sqrt[2] z^(11/4))

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]