Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8702)

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`=-5/2

http://functions.wolfram.com/07.22.03.8702.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), 13/4}, z] == ((-2 Sqrt[z] (-288735522075 - 1238431194000 z + 1008306351360 z^2 + 672092467200 z^3 + 165584240640 z^4 + 203663867904 z^5 - 18673041408 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (-481225870125 + 1377825649200 z + 2221835616000 z^2 + 1014646026240 z^3 + 317977067520 z^4 + 187721318400 z^5 - 18438160384 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-1443677610375 + 1053631378800 z + 1943349408000 z^2 + 946944552960 z^3 + 300760104960 z^4 + 189923328000 z^5 - 18471714816 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(1859803545600 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]