Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9602)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9602.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 1/4}, z] == (1/(36546681600 z^(7/2))) ((1733106375 - 1733106375 E^(4 Sqrt[z]) + 3466212750 Sqrt[z] + 3466212750 E^(4 Sqrt[z]) Sqrt[z] + 1706443200 z - 1706443200 E^(4 Sqrt[z]) z - 1208730600 z^(3/2) - 1208730600 E^(4 Sqrt[z]) z^(3/2) - 474012000 z^2 + 474012000 E^(4 Sqrt[z]) z^2 + 1896048000 z^(5/2) + 1896048000 E^(4 Sqrt[z]) z^(5/2) - 3539289600 z^3 + 3539289600 E^(4 Sqrt[z]) z^3 + 7767429120 z^(7/2) + 7767429120 E^(4 Sqrt[z]) z^(7/2) - 41093775360 z^4 + 41093775360 E^(4 Sqrt[z]) z^4 - 4443318000 z^(9/2) - 4443318000 E^(4 Sqrt[z]) z^(9/2) + 18903234240 z^5 - 18903234240 E^(4 Sqrt[z]) z^5 + 409547520 z^(11/2) + 409547520 E^(4 Sqrt[z]) z^(11/2) - 1668148224 z^6 + 1668148224 E^(4 Sqrt[z]) z^6 - 10211328 z^(13/2) - 10211328 E^(4 Sqrt[z]) z^(13/2) + 41041920 z^7 - 41041920 E^(4 Sqrt[z]) z^7 + 65536 z^(15/2) + 65536 E^(4 Sqrt[z]) z^(15/2) - 262144 z^8 + 262144 E^(4 Sqrt[z]) z^8 - 4 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (11025716625 - 4800312000 z + 418936320 z^2 - 10272768 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 4 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (11025716625 - 4800312000 z + 418936320 z^2 - 10272768 z^3 + 65536 z^4) 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]