Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8375)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8375.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 21/4}, -z] == (Sqrt[Pi] (2816578925901365625 + 4952226682903500000 z + 13205937821076000000 z^2 - 112690669406515200000 z^3 + 631067748676485120000 z^4 + 448759287947722752000 z^5 + 65752276622376960000 z^6 + 3214778994524160000 z^7 + 61233885609984000 z^8 + 458358909829120 z^9 + 1099511627776 z^10) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-2816578925901365625 - 1947875828608710000 z - 8686572433418880000 z^2 + 23357359856388096000 z^3 + 24824371943050444800 z^4 + 3934369777818009600 z^5 + 197439246292746240 z^6 + 3800514554757120 z^7 + 28583007354880 z^8 + 68719476736 z^9)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (938859641967121875 + 1221549248449530000 z - 9053713642393728000 z^2 + 35460248495022489600 z^3 + 27350461646703820800 z^4 + 4073343236702208000 z^5 + 200217678084833280 z^6 + 3821774642872320 z^7 + 28634546962432 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]]))/(632774439343226880000 z^(17/4))

Standard Form

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MathML Form

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</apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 632774439343226880000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]