Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8807)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.8807.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 21/4}, -z] == -(((2 Sqrt[z] (5574039253657875 + 8384879561058000 z + 3252316920652800 z^2 - 5629339208908800 z^3 + 5406448907059200 z^4 + 30649409832222720 z^5 + 9492197497896960 z^6 + 646828517228544 z^7 + 12897786789888 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (9290065422763125 + 20581068013506000 z + 5420528201088000 z^2 + 3604299271372800 z^3 - 10806555407155200 z^4 + 23219249872896000 z^5 + 8944816666705920 z^6 + 635644422389760 z^7 + 12837657247744 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (27870196268289375 + 2286785334834000 z + 2323083514752000 z^2 + 3153761862451200 z^3 - 9902309385830400 z^4 + 24129758822400000 z^5 + 9019565203783680 z^6 + 637222822871040 z^7 + 12846247182336 z^8 + 68719476736 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(7654379146444800 Sqrt[2] z^(15/4)))

Standard Form

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MathML Form

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<ci> Gamma </ci> <cn type='rational'> 5 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 7654379146444800 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]