Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7470)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-15/4

http://functions.wolfram.com/07.22.03.7470.01

Input Form

HypergeometricPFQ[{5}, {-(15/4), 19/4}, z] == (1/(3145728 z^(15/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (-156080925 - 54054000 z - 9313920 z^2 - 1056768 z^3 + 31232 z^4 + 8192 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-468242775 + 936485550 Sqrt[z] - 964863900 z + 681080400 z^(3/2) - 371725200 z^2 + 168315840 z^(5/2) - 66890880 z^3 + 24675840 z^(7/2) - 8144640 z^4 + 1720320 z^(9/2) + 172032 z^5 - 262144 z^(11/2) + 65536 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (468242775 + 936485550 Sqrt[z] + 964863900 z + 681080400 z^(3/2) + 371725200 z^2 + 168315840 z^(5/2) + 66890880 z^3 + 24675840 z^(7/2) + 8144640 z^4 + 1720320 z^(9/2) - 172032 z^5 - 262144 z^(11/2) - 65536 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> <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]