Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6806)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-23/4

http://functions.wolfram.com/07.22.03.6806.01

Input Form

HypergeometricPFQ[{3}, {-(23/4), 19/4}, z] == (1/(1789952 z^(15/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (16804712925 + 4318914600 z + 469188720 z^2 + 23788928 z^3 + 505088 z^4 + 2048 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (50414138775 - 100828277550 Sqrt[z] + 99380981700 z - 64324260000 z^(3/2) + 30702672000 z^2 - 11489718240 z^(5/2) + 3491167680 z^3 - 876395520 z^(7/2) + 181843200 z^4 - 30553600 z^(9/2) + 3949568 z^5 - 352256 z^(11/2) + 16384 z^6) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (50414138775 + 100828277550 Sqrt[z] + 99380981700 z + 64324260000 z^(3/2) + 30702672000 z^2 + 11489718240 z^(5/2) + 3491167680 z^3 + 876395520 z^(7/2) + 181843200 z^4 + 30553600 z^(9/2) + 3949568 z^5 + 352256 z^(11/2) + 16384 z^6) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]