Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8130)

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`=-5/2

http://functions.wolfram.com/07.22.03.8130.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 17/4}, z] == -((13 (-4 z^(1/4) (4642953983600625 + 6190605311467500 Sqrt[z] + 1722603217104000 z - 1476517043232000 z^(3/2) - 11512803456000 z^2 + 1389909362688000 z^(5/2) - 232213008384000 z^3 + 1018143970099200 z^(7/2) - 75134948474880 z^4 + 326066480087040 z^(9/2) - 16550933299200 z^5 + 95794967347200 z^(11/2) + 11424277463040 z^6 - 47141024169984 z^(13/2) - 496068722688 z^7 + 1997159792640 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (4642953983600625 - 6190605311467500 Sqrt[z] + 1722603217104000 z + 1476517043232000 z^(3/2) - 11512803456000 z^2 - 1389909362688000 z^(5/2) - 232213008384000 z^3 - 1018143970099200 z^(7/2) - 75134948474880 z^4 - 326066480087040 z^(9/2) - 16550933299200 z^5 - 95794967347200 z^(11/2) + 11424277463040 z^6 + 47141024169984 z^(13/2) - 496068722688 z^7 - 1997159792640 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (4642953983600625 - 3229881032070000 z + 2175919853184000 z^2 - 5415622745702400 z^3 - 3938634724147200 z^4 - 1286084807884800 z^5 - 415704180326400 z^6 + 190036196720640 z^7 - 8001524072448 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (4642953983600625 - 3229881032070000 z + 2175919853184000 z^2 - 5415622745702400 z^3 - 3938634724147200 z^4 - 1286084807884800 z^5 - 415704180326400 z^6 + 190036196720640 z^7 - 8001524072448 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(374053855769395200 z^(13/4)))

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]