Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8508)

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`=11/2

http://functions.wolfram.com/07.22.03.8508.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 11/4}, z] == ((2 z (-3007944762322500 + 4174290690570000 z + 38607312504135375 z^2 + 293042809837206000 z^3 - 168228375504134400 z^4 + 21702584493158400 z^5 - 963657051340800 z^6 + 16962315878400 z^7 - 118698803200 z^8 + 268435456 z^9) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (-18047668573935000 + 21608092986480000 z + 87534979421014125 z^2 + 215413596099702000 z^3 - 156103182670406400 z^4 + 21127451269017600 z^5 - 953251858022400 z^6 + 16888580014080 z^7 - 118531031040 z^8 + 268435456 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (6767875715225625 - 6813915686077500 z + 21460765079754000 z^2 + 72757783096873875 z^3 + 257968868657900400 z^4 - 163150057625068800 z^5 + 21468082635878400 z^6 - 959462344949760 z^7 + 16932746035200 z^8 - 118631694336 z^9 + 268435456 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(396405409308480000 Sqrt[2] z^(15/4))

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]