Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6510)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=-23/4

http://functions.wolfram.com/07.22.03.6510.01

Input Form

HypergeometricPFQ[{2}, {-(23/4), 7/4}, z] == (1/(504735 z^(3/4))) ((E^(2 Sqrt[z]) z^(3/4) (-215985 + 248160 z + 52992 z^2 + 1024 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-135135 + 270270 Sqrt[z] - 166320 z - 27720 z^(3/2) + 100800 z^2 - 68544 z^(5/2) + 25088 z^3 - 5248 z^(7/2) + 512 z^4) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (-135135 - 270270 Sqrt[z] - 166320 z + 27720 z^(3/2) + 100800 z^2 + 68544 z^(5/2) + 25088 z^3 + 5248 z^(7/2) + 512 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]