Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8503)

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/07.22.03.8503.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 5/4}, -z] == (Sqrt[Pi] z^(17/4) (1154094836288625 + 1758620702916000 z + 401970446380800 z^2 + 26882036121600 z^3 + 651685724160 z^4 + 5932843008 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 (Sqrt[z] (33483615165000 + 7849638720000 z + 9157911840000 z^2 + 23444254310400 z^3 + 91400318808975 z^4 + 23686703741520 z^5 + 1643276736000 z^6 + 40386600960 z^7 + 369819648 z^8 + 1048576 z^9) Cos[2 Sqrt[z]] - 4 (4185451895625 - 4599397687500 z - 1651694814000 z^2 + 488421964800 z^3 + 58610635776000 z^4 + 105799764433275 z^5 + 24823926242640 z^6 + 1672639741440 z^7 + 40661262336 z^8 + 370606080 z^9 + 1048576 z^10) Sin[2 Sqrt[z]]))/ (1478435092992000 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]