Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9oo)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9oo.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 23/4}, z] == (4 z^(1/4) (132067978875 - 3985707505500 Sqrt[z] + 548847381600 z - 2546428752000 z^(3/2) + 193495599360 z^2 - 866345518080 z^(5/2) + 46092533760 z^3 - 278382182400 z^(7/2) - 36849254400 z^4 + 152527699968 z^(9/2) + 1767899136 z^5 - 7121928192 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (-132067978875 - 3985707505500 Sqrt[z] - 548847381600 z - 2546428752000 z^(3/2) - 193495599360 z^2 - 866345518080 z^(5/2) - 46092533760 z^3 - 278382182400 z^(7/2) + 36849254400 z^4 + 152527699968 z^(9/2) - 1767899136 z^5 - 7121928192 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-6374765194875 - 15866082262800 z - 9890544787200 z^2 - 3425296896000 z^3 - 1217883340800 z^4 + 615351582720 z^5 - 28538044416 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-6374765194875 - 15866082262800 z - 9890544787200 z^2 - 3425296896000 z^3 - 1217883340800 z^4 + 615351582720 z^5 - 28538044416 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(3556232921088 z^(19/4))

Standard Form

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MathML 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]