Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7670)

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=-23/4

http://functions.wolfram.com/07.22.03.7670.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), 7/4}, z] == (1/(15505459200 z^(3/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (521118675 + 741460500 z - 105809760 z^2 - 8808896 z^3 + 1153024 z^4 + 16384 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-1343917575 + 2687835150 Sqrt[z] + 1654052400 z - 6891885000 z^(3/2) + 5814244800 z^2 - 1483634880 z^(5/2) - 700976640 z^3 + 565618560 z^(7/2) - 81600000 z^4 - 39342080 z^(9/2) + 9846784 z^5 + 2588672 z^(11/2) + 131072 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (1343917575 + 2687835150 Sqrt[z] - 1654052400 z - 6891885000 z^(3/2) - 5814244800 z^2 - 1483634880 z^(5/2) + 700976640 z^3 + 565618560 z^(7/2) + 81600000 z^4 - 39342080 z^(9/2) - 9846784 z^5 + 2588672 z^(11/2) - 131072 z^6) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1343917575 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </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]