Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8968)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8968.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(9/4)}, z] == (1/(243338800320 z^(5/2))) ((-41247931725 + 41247931725 E^(4 Sqrt[z]) - 82495863450 Sqrt[z] - 82495863450 E^(4 Sqrt[z]) Sqrt[z] - 37629692100 z + 37629692100 E^(4 Sqrt[z]) z + 34735100400 z^(3/2) + 34735100400 E^(4 Sqrt[z]) z^(3/2) - 18525386880 z^2 + 18525386880 E^(4 Sqrt[z]) z^2 + 8973296640 z^(5/2) + 8973296640 E^(4 Sqrt[z]) z^(5/2) - 4508421120 z^3 + 4508421120 E^(4 Sqrt[z]) z^3 + 2543063040 z^(7/2) + 2543063040 E^(4 Sqrt[z]) z^(7/2) - 1734082560 z^4 + 1734082560 E^(4 Sqrt[z]) z^4 + 1577189376 z^(9/2) + 1577189376 E^(4 Sqrt[z]) z^(9/2) - 2295595008 z^5 + 2295595008 E^(4 Sqrt[z]) z^5 + 9666822144 z^(11/2) + 9666822144 E^(4 Sqrt[z]) z^(11/2) + 168689664 z^6 - 168689664 E^(4 Sqrt[z]) z^6 - 681050112 z^(13/2) - 681050112 E^(4 Sqrt[z]) z^(13/2) - 2097152 z^7 + 2097152 E^(4 Sqrt[z]) z^7 + 8388608 z^(15/2) + 8388608 E^(4 Sqrt[z]) z^(15/2) + 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (298809 - 20832 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (298809 - 20832 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]