Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7540)

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=-7/4

http://functions.wolfram.com/07.22.03.7540.01

Input Form

HypergeometricPFQ[{5}, {-(7/4), 23/4}, z] == (1/(33554432 z^(19/4))) ((1045 (-16 E^(2 Sqrt[z]) z^(3/4) (156080925 + 46195380 z + 6199200 z^2 + 479808 z^3 + 25600 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-468242775 + 936485550 Sqrt[z] - 941288040 z + 633928680 z^(3/2) - 321965280 z^2 + 131664960 z^(5/2) - 45239040 z^3 + 13474944 z^(7/2) - 3575808 z^4 + 872448 z^(9/2) - 196608 z^5 + 32768 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (468242775 + 936485550 Sqrt[z] + 941288040 z + 633928680 z^(3/2) + 321965280 z^2 + 131664960 z^(5/2) + 45239040 z^3 + 13474944 z^(7/2) + 3575808 z^4 + 872448 z^(9/2) + 196608 z^5 + 32768 z^(11/2)) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<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]