Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8953)

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`=5/2

http://functions.wolfram.com/07.22.03.8953.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 23/4}, -z] == (Sqrt[Pi] (-1331337837123669375 - 1577881881035460000 z - 2065590826082784000 z^2 - 12590267892314112000 z^3 + 39169722331643904000 z^4 + 107436952681080422400 z^5 + 26045321862080102400 z^6 + 1763915977960980480 z^7 + 42848161407959040 z^8 + 389639433093120 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-443779279041223125 - 323090099450118000 z - 480878287553664000 z^2 + 1645883214435532800 z^3 + 6448722445851033600 z^4 + 1608200451375759360 z^5 + 109752435647447040 z^6 + 2673472186613760 z^7 + 24339579666432 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (1331337837123669375 + 157788188103546000 z + 743175535310208000 z^2 - 354037253997772800 z^3 + 5519225534260838400 z^4 + 1533596485917081600 z^5 + 107821741815889920 z^6 + 2655433323970560 z^7 + 24288040058880 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]]))/(103238864192353075200 z^(19/4))

Standard Form

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MathML Form

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<apply> <power /> <apply> <times /> <cn type='integer'> 103238864192353075200 </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]