Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8857)

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/07.22.03.8857.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 23/4}, -z] == (Sqrt[Pi] (-473793336560919375 - 297282093528420000 z - 149680494643680000 z^2 - 101370917007360000 z^3 - 189225711747072000 z^4 + 3633133665543782400 z^5 + 3229452147150028800 z^6 + 468673327477555200 z^7 + 19664615138918400 z^8 + 274190712176640 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-157931112186973125 - 26896951319238000 z - 16261584603264000 z^2 - 17345690243481600 z^3 + 198608073198796800 z^4 + 196811226139852800 z^5 + 29068492674170880 z^6 + 1225853459496960 z^7 + 17124034609152 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (473793336560919375 - 208097465469894000 z - 39070040929920000 z^2 + 7884404656128000 z^3 + 113535427048243200 z^4 + 178387064664883200 z^5 + 28200851566755840 z^6 + 1213226255646720 z^7 + 17072495001600 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]]))/(1994953897436774400 z^(19/4))

Standard Form

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MathML Form

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<power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1994953897436774400 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <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]