Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8sk)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8sk.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, 19/4}, z] == (-4 (5072191488000 + 10144382976000 Sqrt[z] - 2020056272325 z + 20493752724900 z^(3/2) - 2184055604640 z^2 + 12774417102720 z^(5/2) - 812365182720 z^3 + 6651150105600 z^(7/2) + 1498510540800 z^4 - 6361587843072 z^(9/2) - 132064149504 z^5 + 536910495744 z^(11/2) + 2942304256 z^6 - 11819548672 z^(13/2) - 16777216 z^7 + 67108864 z^(15/2) + E^(4 Sqrt[z]) (-5072191488000 + 10144382976000 Sqrt[z] + 2020056272325 z + 20493752724900 z^(3/2) + 2184055604640 z^2 + 12774417102720 z^(5/2) + 812365182720 z^3 + 6651150105600 z^(7/2) - 1498510540800 z^4 - 6361587843072 z^(9/2) + 132064149504 z^5 + 536910495744 z^(11/2) - 2942304256 z^6 - 11819548672 z^(13/2) + 16777216 z^7 + 67108864 z^(15/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (57089563856325 + 83039365609200 z + 51764799340800 z^2 + 30675436646400 z^3 - 25831946649600 z^4 + 2156405981184 z^5 - 47328526336 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (57089563856325 + 83039365609200 z + 51764799340800 z^2 + 30675436646400 z^3 - 25831946649600 z^4 + 2156405981184 z^5 - 47328526336 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (130913824407552 z^(9/2))

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]