Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8606)

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`=-9/2

http://functions.wolfram.com/07.22.03.8606.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 13/4}, z] == ((-2 Sqrt[z] (-8538321867075 - 7138403672400 z + 15053623200000 z^2 + 4607995392000 z^3 + 580442849280 z^4 + 43797970944 z^5 + 2466250752 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (-14230536445125 + 35418224041200 z + 20795654880000 z^2 + 5216008089600 z^3 + 624166502400 z^4 + 46352302080 z^5 + 2701131776 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-42691609335375 + 15179238874800 z + 19376931974400 z^2 + 5100350976000 z^3 + 616528281600 z^4 + 45911900160 z^5 + 2667577344 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(22317642547200 Sqrt[2] z^(7/4))

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]