Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8876)

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`=3/2

http://functions.wolfram.com/07.22.03.8876.01

Input Form

HypergeometricPFQ[{-(21/4)}, {3/2, -(5/4)}, z] == (1/(90852300 Sqrt[z])) ((-13157235 + 13157235 E^(4 Sqrt[z]) + 19111680 Sqrt[z] + 19111680 E^(4 Sqrt[z]) Sqrt[z] - 21924000 z + 21924000 E^(4 Sqrt[z]) z + 27578880 z^(3/2) + 27578880 E^(4 Sqrt[z]) z^(3/2) - 49271040 z^2 + 49271040 E^(4 Sqrt[z]) z^2 + 233275392 z^(5/2) + 233275392 E^(4 Sqrt[z]) z^(5/2) + 14311584 z^3 - 14311584 E^(4 Sqrt[z]) z^3 - 59364480 z^(7/2) - 59364480 E^(4 Sqrt[z]) z^(7/2) - 734208 z^4 + 734208 E^(4 Sqrt[z]) z^4 + 2961408 z^(9/2) + 2961408 E^(4 Sqrt[z]) z^(9/2) + 8192 z^5 - 8192 E^(4 Sqrt[z]) z^5 - 32768 z^(11/2) - 32768 E^(4 Sqrt[z]) z^(11/2) - 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-30421755 + 7488432 z - 370944 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-30421755 + 7488432 z - 370944 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

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]