Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6518)

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/07.22.03.6518.01

Input Form

HypergeometricPFQ[{2}, {-(23/4), 23/4}, z] == (1/(94208 z^(19/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (68746552875 + 14840525700 z + 1288872000 z^2 + 43243200 z^3 + 515072 z^4 + 1024 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (206239658625 - 412479317250 Sqrt[z] + 398075277600 z - 246178132200 z^(3/2) + 109167458400 z^2 - 36756720000 z^(5/2) + 9686476800 z^3 - 2023781760 z^(7/2) + 334414080 z^4 - 42831360 z^(9/2) + 4055040 z^5 - 256000 z^(11/2) + 8192 z^6) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (206239658625 + 412479317250 Sqrt[z] + 398075277600 z + 246178132200 z^(3/2) + 109167458400 z^2 + 36756720000 z^(5/2) + 9686476800 z^3 + 2023781760 z^(7/2) + 334414080 z^4 + 42831360 z^(9/2) + 4055040 z^5 + 256000 z^(11/2) + 8192 z^6) 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]