Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8183)

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/07.22.03.8183.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 21/4}, -z] == (17 (Sqrt[Pi] (784659223228505625 + 419884534169100000 z + 176793488071200000 z^2 + 100575850991616000 z^3 + 256011257069568000 z^4 - 234067435035033600 z^5 + 148614244466688000 z^6 + 123523527868416000 z^7 + 9881882229473280 z^8 + 205471235440640 z^9 + 1099511627776 z^10) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-784659223228505625 + 417085303941306000 z + 58519579966848000 z^2 - 1959269824512000 z^3 - 9363676092825600 z^4 + 3943013548032000 z^5 + 7186341628477440 z^6 + 605831980646400 z^7 + 12777527705600 z^8 + 68719476736 z^9)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (261553074409501875 + 20394391659642000 z + 14272736429952000 z^2 + 15340357070438400 z^3 - 14417414465126400 z^4 + 8063703318528000 z^5 + 7609509992202240 z^6 + 615237959024640 z^7 + 12829067313152 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/(5984861692310323200 z^(17/4))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 5984861692310323200 </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]