Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8421)

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`=7/2

http://functions.wolfram.com/07.22.03.8421.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 19/4}, -z] == ((2 Sqrt[z] (582574444502675625 + 7384320231618330000 z - 17796058700874854400 z^2 + 100132908145824153600 z^3 + 51900574973666918400 z^4 + 6271409468850831360 z^5 + 266283205609390080 z^6 + 4537408536182784 z^7 + 30979599106048 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - (1747723333508026875 + 19489763234271330000 z - 37049000509967846400 z^2 + 75740959430251315200 z^3 + 48380031626998579200 z^4 + 6112254225631150080 z^5 + 263498561885306880 z^6 + 4518161713987584 z^7 + 30936649433088 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-1747723333508026875 + 15764960165261907600 z - 30377259527834419200 z^2 + 89192347063710105600 z^3 + 50428941795606528000 z^4 + 6206555345827921920 z^5 + 265160828381036544 z^6 + 4529690479951872 z^7 + 30962419236864 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (131999737315590144000 Sqrt[2] z^(13/4))

Standard Form

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MathML Form

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</apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 131999737315590144000 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <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]