Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7508)

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=-11/4

http://functions.wolfram.com/07.22.03.7508.01

Input Form

HypergeometricPFQ[{5}, {-(11/4), 23/4}, z] == -((1/(16777216 z^(19/4))) ((95 (16 E^(2 Sqrt[z]) z^(3/4) (2341213875 + 689729040 z + 91808640 z^2 + 6967296 z^3 + 358912 z^4 + 8192 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (7023641625 - 14047283250 Sqrt[z] + 14109715620 z - 9489720240 z^(3/2) + 4809475440 z^2 - 1960580160 z^(5/2) + 670481280 z^3 - 198277632 z^(7/2) + 51980544 z^4 - 12386304 z^(9/2) + 2727936 z^5 - 524288 z^(11/2) + 65536 z^6) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (7023641625 + 14047283250 Sqrt[z] + 14109715620 z + 9489720240 z^(3/2) + 4809475440 z^2 + 1960580160 z^(5/2) + 670481280 z^3 + 198277632 z^(7/2) + 51980544 z^4 + 12386304 z^(9/2) + 2727936 z^5 + 524288 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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</ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </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]