Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9py)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a9py.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(11/2), 21/4}, z] == (221 (-4 z^(1/4) (67469484557475 + 89959312743300 Sqrt[z] + 59192163177840 z + 24090541231680 z^(3/2) + 6272733519360 z^2 + 1022514554880 z^(5/2) + 91341250560 z^3 - 22037889024 z^(7/2) + 586088448 z^4 - 2309750784 z^(9/2) + 11534336 z^5 - 46137344 z^(11/2) + E^(4 Sqrt[z]) (67469484557475 - 89959312743300 Sqrt[z] + 59192163177840 z - 24090541231680 z^(3/2) + 6272733519360 z^2 - 1022514554880 z^(5/2) + 91341250560 z^3 + 22037889024 z^(7/2) + 586088448 z^4 + 2309750784 z^(9/2) + 11534336 z^5 + 46137344 z^(11/2))) + 11 E^(2 Sqrt[z]) Sqrt[2 Pi] (6133589505225 - 1161389728800 z + 147478060800 z^2 - 20298055680 z^3 + 9021358080 z^4 + 836763648 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + 11 E^(2 Sqrt[z]) Sqrt[2 Pi] (6133589505225 - 1161389728800 z + 147478060800 z^2 - 20298055680 z^3 + 9021358080 z^4 + 836763648 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (72567767433216 z^(17/4))

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]