Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8327)

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`=3/2

http://functions.wolfram.com/07.22.03.8327.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 21/4}, -z] == (Sqrt[Pi] (-1068357523617759375 - 1195365061390500000 z - 1366131498732000000 z^2 - 3885885151948800000 z^3 + 108804784254566400000 z^4 + 139270123845844992000 z^5 + 29475158485893120000 z^6 + 1884525617479680000 z^7 + 44341779234816000 z^8 + 395136991232000 z^9 + 1099511627776 z^10) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((1068357523617759375 + 55783702864890000 z + 380492921128320000 z^2 + 2720119606364160000 z^3 + 7332758772911308800 z^4 + 1741227564780748800 z^5 + 115273595973795840 z^6 + 2748462315601920 z^7 + 24631637442560 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-356119174539253125 - 235657683531270000 z - 299536980462720000 z^2 + 5696494959878553600 z^3 + 8400967762644172800 z^4 + 1821189262698086400 z^5 + 117273175712071680 z^6 + 2766758876282880 z^7 + 24683177050112 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]]))/(130918849519288320000 z^(17/4))

Standard Form

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MathML Form

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<apply> <power /> <apply> <times /> <cn type='integer'> 130918849519288320000 </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]