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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-9/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), 23/4}, z] == -((1/(63417876480 z^(19/4))) ((19 (4 z^(1/4) (640591234408125 + 854121645877500 Sqrt[z] + 683297316702000 z + 390455609544000 z^(3/2) + 173535826464000 z^2 + 63103936896000 z^(5/2) + 19416595968000 z^3 + 5177758924800 z^(7/2) + 1218296217600 z^4 + 256066191360 z^(9/2) + 48019537920 z^5 + 7738490880 z^(11/2) + 956301312 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (-640591234408125 + 854121645877500 Sqrt[z] - 683297316702000 z + 390455609544000 z^(3/2) - 173535826464000 z^2 + 63103936896000 z^(5/2) - 19416595968000 z^3 + 5177758924800 z^(7/2) - 1218296217600 z^4 + 256066191360 z^(9/2) - 48019537920 z^5 + 7738490880 z^(11/2) - 956301312 z^6 + 67108864 z^(13/2))) - 640591234408125 E^(2 Sqrt[z]) Sqrt[2 Pi] Erf[Sqrt[2] z^(1/4)] + 640591234408125 E^(2 Sqrt[z]) Sqrt[2 Pi] Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))

Standard Form

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MathML Form

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</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]