Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adr6)

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=11/4, b_1`>=-11/2

For fixed z and a₁=11/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.adr6.01

Input Form

HypergeometricPFQ[{11/4}, {-(9/2), 19/4}, z] == (1/(1056964608 z^(15/4))) ((11 (-4 z^(1/4) (-1154218440375 - 1538957920500 Sqrt[z] - 1180291694400 z - 635690764800 z^(3/2) - 258410880000 z^2 - 82691481600 z^(5/2) - 21202944000 z^3 - 4329701376 z^(7/2) - 677117952 z^4 - 73400320 z^(9/2) - 4194304 z^5 + E^(4 Sqrt[z]) (1154218440375 - 1538957920500 Sqrt[z] + 1180291694400 z - 635690764800 z^(3/2) + 258410880000 z^2 - 82691481600 z^(5/2) + 21202944000 z^3 - 4329701376 z^(7/2) + 677117952 z^4 - 73400320 z^(9/2) + 4194304 z^5)) + 3179665125 E^(2 Sqrt[z]) Sqrt[2 Pi] (-363 + 16 z) Erf[Sqrt[2] z^(1/4)] - 3179665125 E^(2 Sqrt[z]) Sqrt[2 Pi] (-363 + 16 z) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> <cn type='integer'> -363 </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> </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]