Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7748)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-15/4

http://functions.wolfram.com/07.22.03.7748.01

Input Form

HypergeometricPFQ[{6}, {-(15/4), -(5/4)}, z] == (1/4158000) ((48 E^(2 Sqrt[z]) (86625 + 110880 z + 564480 z^2 - 25305 z^3 + 388480 z^4 + 5888 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (10094175 - 20188350 Sqrt[z] + 3105900 z + 20706000 z^(3/2) + 9744000 z^2 + 1784832 z^(5/2) + 142336 z^3 + 4096 z^(7/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(9/4) (-10094175 - 20188350 Sqrt[z] - 3105900 z + 20706000 z^(3/2) - 9744000 z^2 + 1784832 z^(5/2) - 142336 z^3 + 4096 z^(7/2)) 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]