Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8809)

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/07.22.03.8809.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 23/4}, -z] == -((19 (Sqrt[Pi] (523666319356805625 + 265989241578060000 z + 102412970019360000 z^2 + 48017802792960000 z^3 + 49796239933440000 z^4 - 191217561344409600 z^5 + 509913496918425600 z^6 + 172669120649625600 z^7 + 11384777185689600 z^8 + 216466351718400 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (174555439785601875 + 8866308052602000 z + 6502410794880000 z^2 + 5892555058790400 z^3 - 14930564176281600 z^4 + 30105764049715200 z^5 + 10663779347988480 z^6 + 709040044769280 z^7 + 13516262080512 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (-523666319356805625 + 292588165735866000 z + 39447958822272000 z^2 + 5038905231360000 z^3 - 19254546107596800 z^4 + 23968657598054400 z^5 + 10172417641021440 z^6 + 699118670315520 z^7 + 13464722472960 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/(3989907794873548800 z^(19/4)))

Standard Form

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MathML Form

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</ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 3989907794873548800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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]