Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8483)

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`=11/2

http://functions.wolfram.com/07.22.03.8483.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(15/4)}, -z] == (2 Sqrt[z] (-794419697049103125 + 247611334145175000 z + 10119492583200000 z^2 - 647647525324800 z^3 + 38391658905600 z^4 - 3046535331840 z^5 + 396361728000 z^6 - 110729625600 z^7 + 124554051584 z^8 + 2147483648 z^9) Cos[2 Sqrt[z]] + 2147483648 Sqrt[Pi] z^(37/4) (943 + 16 z) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (794419697049103125 - 1306837596877312500 z + 37568616215130000 z^2 - 5424048024595200 z^3 + 308403583488000 z^4 - 20590682112000 z^5 + 2038290186240 z^6 - 371699220480 z^7 + 182804545536 z^8 - 1009317314560 z^9 - 17179869184 z^10) Sin[2 Sqrt[z]])/ (14229937770048000 z^(9/2))

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]