Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afi0)

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.afi0.01

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), -(23/4)}, z] == -((1/(4958150707125 z^(1/4))) (Sqrt[2] (3 (-1652716902375 + 3002036499000 z - 547483860000 z^2 - 634594625280 z^3 - 183571153920 z^4 - 43145625600 z^5 + 63583027200 z^6 + 96888422400 z^7 + 1543503872 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-4958150707125 + 2395241887500 z + 2810417148000 z^2 + 929859860160 z^3 + 198402462720 z^4 + 16690544640 z^5 + 190749081600 z^6 + 26537361408 z^7 + 67108864 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (-1652716902375 - 1405208574000 z - 517068090000 z^2 - 124347041280 z^3 - 29662617600 z^4 - 19074908160 z^5 + 17862492160 z^6 + 369098752 z^7) 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]