Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8354)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8354.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 1/4}, z] == (1/(775232640000 z^(3/2))) ((-4 (-1817046000 - 3634092000 Sqrt[z] + 17443641600 z - 57171340800 z^(3/2) + 374079283200 z^2 + 80920682325 z^(5/2) - 362475651300 z^3 - 15255863040 z^(7/2) + 63285361920 z^4 + 798507520 z^(9/2) - 3234150400 z^5 - 13598720 z^(11/2) + 54591488 z^6 + 65536 z^(13/2) - 262144 z^7 + E^(4 Sqrt[z]) (1817046000 - 3634092000 Sqrt[z] - 17443641600 z - 57171340800 z^(3/2) - 374079283200 z^2 + 80920682325 z^(5/2) + 362475651300 z^3 - 15255863040 z^(7/2) - 63285361920 z^4 + 798507520 z^(9/2) + 3234150400 z^5 - 13598720 z^(11/2) - 54591488 z^6 + 65536 z^(13/2) + 262144 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (-1698294472875 + 1493006130000 z - 255487680000 z^2 + 12977152000 z^3 - 218562560 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (-1698294472875 + 1493006130000 z - 255487680000 z^2 + 12977152000 z^3 - 218562560 z^4 + 1048576 z^5) 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]