Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bb)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8bb.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 21/4}, -z] == (Sqrt[Pi] (306917176190625 - 3021953734800000 z + 3760653536640000 z^2 - 2674242514944000 z^3 + 4114219253760000 z^4 + 1032588361728000 z^5 + 56195284992000 z^6 + 934155386880 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-306917176190625 + 419426162694000 z - 258671335507200 z^2 + 207815376384000 z^3 + 61450745610240 z^4 + 3458460549120 z^5 + 58133053440 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-263932511275125 + 285299308047600 z - 196158699475200 z^2 + 246338742988800 z^3 + 63901499719680 z^4 + 3501368279040 z^5 + 58334380032 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (3138762099916800 z^(17/4))

Standard Form

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MathML Form

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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]